Bicubic G1 interpolation of arbitrary quad meshes using a 4-split

4Bile acids,obesity,and the metabolic syndromeHuijuan Ma,MD,Adult Endocrinologist a ,Mary Elizabeth Patti,MD,Investigator andAdult Endocrinologist b ,*aDepartment of Endocrinology and Metabolism,Hebei General Hospital,Shijiazhuang,Hebei 050051,China b Research Division,Joslin Diabetes Center,and Harvard Medical School,Boston,MA 02215,USAKeywords:Bile acidsFXRTGR5ObesityInsulin resistance a b s t r a c tBile acids are increasingly recognized as key regulators of systemic metabolism.While bile acids have long been known to play important and direct roles in nutrient absorption,bile acids also serve as signalling molecules.Bile acid interactions with the nuclear hormone receptor farnesoid X receptor (FXR)and themembrane receptor G-protein-coupled bile acid receptor 5(TGR5)can regulate incretin hormone and fibroblast growth factor 19(FGF19)secretion,cholesterol metabolism,and systemic energyexpenditure.Bile acid levels and distribution are altered in type 2diabetes and increased following bariatric procedures,in parallelwith reduced body weight and improved insulin sensitivity andglycaemic control.Thus,modulation of bile acid levels andsignalling,using bile acid binding resins,TGR5agonists,and FXRagonists,may serve as a potent therapeutic approach for thetreatment of obesity,type 2diabetes,and other components of themetabolic syndrome in humans.©2014Elsevier Ltd.All rights reserved.IntroductionBile is a mixture of bile acids (BAs),cholesterol,phosphatidylcholine,and bilirubin.Of these,BAs are essential constituents and play critical roles in regulation of metabolism in both humans and animal *Corresponding author.Joslin Diabetes Center,1Joslin Place,Boston,MA 02215,USA.Tel.:þ16173091966;fax:þ16173092593.E-mail address:Mary.Elizabeth.Patti@ (M.E.Patti).Contents lists available at ScienceDirectBest Practice &Research ClinicalGastroenterology/10.1016/j.bpg.2014.07.0041521-6918/©2014Elsevier Ltd.All rights reserved.Best Practice &Research Clinical Gastroenterology 28(2014)573e 583models.Bile acids have long been recognized to aid in the absorption of fat and fat-soluble vitamins and modulate cholesterol levels.However,recent data indicate that bile acids also play an important role in glucose and lipid homeostasis by activating both the nuclear receptor LXR and the cell surface receptor G protein-coupled bile acid receptor 5(TGR5)[1e 3].Moreover,modulation of plasma bile acid levels and the total bile acid pool can affect glycaemic control,body weight,and insulin sensitivity[4e 6].In this review,we will focus on the relation between bile acids and regulation of systemic meta-bolism and the potential for bile acids as a therapeutic approach for obesity,insulin resistance,type 2diabetes (T2D),and other components of the metabolic syndrome.Bile acid synthesis and regulationBile acid synthesisBAs are amphipathic molecules with a steroid backbone which are synthesized from cholesterol in hepatocytes.It is estimated that about half of the 800mg of cholesterol synthesized daily is used for bile acid synthesis,totalling about 200e 600mg daily in humans [7].Bile acids are synthesized from cholesterol through two dominant pathways:the classic pathway and the alternative pathway (Fig.1).In the classic (or neutral)pathway,CYP7A1catalyses the initial and rate-limiting step converting cholesterol into 7a -hydroxycholesterol,with CYP8B1subsequently regulating synthesis of 12a -hydroxysterols including cholic acid (CA).In the alternative (or acidic)pathway,CYP27A1first hydroxylates the cholesterol side chain,converting cholesterol into 27-hydroxycholesterol,which is then 7a -hydroxylated by CYP7B1prior to CYP8B1action.In humans,the classical pathway produces the primary BA cholic acid (CA)and chenodeoxycholic acid (CDCA)in Fig.1.Bile acid synthesis pathway.Cholesterol is converted to two primary bile acids in human liver,CA and CDCA.Key regulatory enzymes in these pathways include CYP7A1,CYP8B1,CYP27A1,and CYP7B1.CYP7A1initiates the classic (neutral)biosynthetic pathway,while CYP27A1initiates the alternative (acidic)pathway in liver and macrophages.CA and CDCA can be conjugated with glycine (G)and taurine (T).In the intestine,conjugated CA and CDCA are deconjugated and then dehydroxylated at the 7a -position to the secondary bile acids DCA and LCA,respectively.H.Ma,M.E.Patti /Best Practice &Research Clinical Gastroenterology 28(2014)573e 583574H.Ma,M.E.Patti/Best Practice&Research Clinical Gastroenterology28(2014)573e583575 roughly equal amounts,whereas the alternative pathway produces mainly CDCA[8].Most bile acids are conjugated with either glycine or taurine,with a3:1predominance of glycine over taurine[3,5,9].Synthesized BA are stored in the gallbladder and secreted into the duodenum in response to feeding,contributing to digestion of lipids and lipid-soluble vitamins.The primary BA CA and CDCA can be dehydroxylated at the7a position by gut microbiota to produce the secondary BAs,predominantly deoxycholic acid(DCA)and lithocholic acid(LCA)[10,11].Thus,bile acid levels and relative composition can be modulated by gut microbiota populations[12].In the terminal ileum,BAs are efficiently absorbed by both active transport and passive diffusion, transported back to the liver via the portal vein,taken up at the sinusoidal membrane of hepatocytes, and secreted into bile again.Each BA molecule may complete4e12cycles of this enterohepatic cir-culation per day[1,13].This process is highly efficient,as only about5%of bile acids are lost in feces [3,14].This process is similar in mice,although different bile acid species dominate.CDCA is efficiently converted into muricholic acid(MCA),and BAs are conjugated to taurine.Given that different BA have different structures,hydrophobicity,and affinities for membrane and nuclear receptors,interindividual differences in BA pool composition resulting from differential regulation of the complex BA synthesis pathway may have functional consequences for systemic metabolism.Regulation of Bile Acid SynthesisBA are potent regulators of their own synthesis,serving to limit excessive accumulation of BA in the circulation via multiple redundant pathways.Feeding bile acids to rats strongly reduces CYP7A1 enzyme activity and bile acid synthesis[8,15].This self-regulation of BA synthesis involves activation of the nuclear receptor FXR(farnesoid X receptor,official gene name NR1H4)[16].FXR knockout mice have increased BA synthesis and Cyp7a1expression,verifying the central role for FXR in mediating bile acid inhibition of Cyp7a1[17].FXR has both direct effects on Cyp7a1expression as well as indirect effects,mediated by induction of small heterodimer partner(SHP)which in turn inhibits trans-activation of CYP7A1and CYP8B1by the transcription factors Hepatocyte Nuclear Factor4a(HNF4a) and liver-related homolog-1(LRH-1)at the bile acid response element.FXR also increases BA conju-gation and upregulates expression of several genes which promote bile acid efflux from hepatocytes into the bile.An additional feedback repression mechanism involves FXR regulation of several indi-vidualfibroblast growth factors(FGFs).For example,bile acid activation of FXR results in secretion of FGF-19from hepatocytes and enterocytes.In turn,FGF-19can bind tofibroblast growth factor receptor 4(FGFR4)receptors on hepatocytes,leading to suppression of CYP7A1expression and bile acid syn-thesis via a SHP-independent,but c-Jun N-terminal kinase(JNK)dependent mechanism[18].Consis-tent with this mechanism,FGFR4knockout mice have increased expression of CYP7A1,in parallel with increased fecal bile acids and bile acid pool size[19].Other nuclear receptors,such as the pregnane X receptor(PXR)[20]and vitamin D receptor(VDR)[21],can also regulate BA synthesis by suppressing CYP7A1.Moreover,activation of the nuclear receptor ROR a can modulate12a-hydroxylase(CYP8B1) expression[22,23].BA differ markedly in their potency to activate FXR.The hydrophobic bile acid CDCA is the most potent BA ligand of FXR,followed by lithocholic acid(LCA),deoxycholic acid(DCA),and CA;by contrast, the hydrophilic bile acids ursodeoxycholic acid(UDCA)and muricholic acid(MCA)do not activate FXR[24].BA are also regulated in response to other elements of systemic metabolism.Early studies showed that the bile acid pool size is increased in insulin-deficient diabetic rats,with a3-fold increase in the cholic acid pool[25].Conversely,insulin treatment reduces bile acid pool size,inhibits CYP7A1and CYP8B1activity,and alters bile acid composition[26].CYP7A1can also be regulated by steroid hor-mones,activated protein kinase C,and proinflammatory cytokines[8].Bile acids and regulation of systemic metabolismFXR and TGR5signalling mechanisms appear to dominate for BA effects on regulation of glucose, lipid,and energy metabolism[1,27e30].As noted above,BA are natural ligands for FXR a,a nuclearreceptor highly expressed in liver,intestine,kidney and adrenal glands [17,27].BAs can also activate TGR5,a membrane-bound G protein-coupled BA receptor.TGR5is expressed in many organs and tissues,with high expression in macrophages/monocytes,placenta,gallbladder,liver and intestine[31,32].BA stimulation of energy expenditure in brown adipose tissue (BAT)and skeletal muscle ap-pears to be mediated via TGR5[2].Bile acids and lipid metabolismBAs exert an important regulatory role in cholesterol and triglyceride (TG)metabolism.Increased bile acid synthesis increases utilization of cholesterol as substrate.Bile acid synthesis rates are correlated with serum triglyceride levels in hyperlipidemic patients [33].Bile acid sequestrants or other interruptions in enterohepatic circulation also increase both bile acid and VLDL triglyceride synthesis.Conversely,CDCA-mediated increases in the BA pool size leads to inhibition of BA synthesis and reduced serum triglycerides in hyperlipidemic patients [34].These effects of BA to modulate TG metabolism are likely mediated via several distinct mechanisms,predominantly BA activation of FXR [35,36].FXR alters the transcription of several genes involved in fatty acid and triglyceride synthesis and lipoprotein metabolism.In mice,administration of FXR ago-nists [GW4064,6a-ethyl-chenodeoxycholic acid]reduces plasma triglyceride and cholesterol levels[37e 41]via repression of the lipogenic genes sterol-regulatory-element-binding protein-1c (SREBP1c)and fatty acid synthase (FAS)in liver [36].FXR also induces expression of peroxisome proliferator activated receptor (PPAR)a ,a nuclear receptor that promotes lipid oxidation [42],and of pyruvate dehydrogenase kinase,isoenzyme 4(PDK4),leading to inhibition of pyruvate dehydrogenase and increased fatty acid oxidation [43].Additional FXR target genes include the apolipoproteins A-V,C-III,apoE,syndecan-1,and the VLDL receptor [1,44].Conversely,FXR-null mice have higher serum TG levels and increased synthesis of apolipoprotein (apo)B-containing lipoproteins [17].Thus,bile acids play central roles in lipid metabolism and in the control of TG levels,in part via FXR and downstream transcriptional targets.Additional effects of BA on lipid metabolism may be independent of FXR.For example,the bile acid tauroursodeoxycholic acid (TUDCA)also acts as a chaperone,modulating endoplasmic reticulum stress[45].TUDCA reduces adipogenesis in human adipocyte stem cells [46].Similarly,in another study,UDCA (but not TUDCA)profoundly inhibits adipogenesis,in parallel with activation of extracellular regulated protein kinases 1and 2(ERK 1/2)[47].Bile acids and glucose metabolismBile acids are also implicated in regulation of glucose metabolism [48e 50].Increasing hepatic bile acid synthesis can inhibit gluconeogenesis and stimulate glycolysis.Effects on glycogen metabolism appear complex [51].Some studies have shown bile acids stimulate glycogen phosphorylase (GP)and glycogen breakdown to glucose-1-P [52],while other data indicate bile acids also activate glycogen synthesis (GS)[53].Additional effects of BA on glucose metabolism and insulin action may also be mediated via reductions in endoplasmic reticulum (ER)stress,a key mediator of insulin resistance [45].In addition to direct effects,many of the bene ficial effects of BA on glucose metabolism are mediated via FXR.FXR is an important regulator of glucose metabolism,as demonstrated by reduced plasma glucose and reduced hepatic glycogen levels in FXR-null mice [49,50,54].Conversely,activation of FXR is associated with increased phosphoenolpyruvate carboxykinase (PEPCK)and glucose-6-phosphatase expression and glucose output from primary rat hepatocytes.However,in vivo pharmacologic stimulation of FXR in two mouse models of obesity and T2D (db/db or KKA(y)mice)causes inhibition of gluconeogenesis,hypoglycemia,and increased insulin sensitivity [49,50].Thus,FXR may have a dominant effect to inhibit gluconeogenesis in diabetes,perhaps via inhibition of PEPCK by SHP-dependent inhibition of HNF4a and FoxO1[55].Activation of FXR can also stimulate the insulin/Akt pathway,promoting glycogen synthesis in liver [55],GLUT2activation in pancreatic b -cells [56],and improving insulin resistance in obese ob/ob mice [57].In this context,inhibition of gluconeogenesis,improved insulin action,and stimulation of glycogen syn-thesis may synergize to improve plasma glucose,insulin secretion,insulin sensitivity,and glucoseH.Ma,M.E.Patti /Best Practice &Research Clinical Gastroenterology 28(2014)573e 583576H.Ma,M.E.Patti/Best Practice&Research Clinical Gastroenterology28(2014)573e583577 tolerance.In parallel,however,GW4064increases susceptibility to high fat diet-induced obesity and diabetes[50,58].These complex data highlight the importance of the specific context in which FXR is activated.Beneficial effects of BA on glucose metabolism may also be mediated via TGR5.TGR5is expressed in many organs and tissues,with highest expression in macrophages/monocytes,placenta,gallbladder, liver and intestine[32].Activation of TGR5in enterocytes can stimulate the secretion of the incretin hormone glucagon-like peptide GLP1,promoting glucose-dependent insulin secretion[59,60].More-over,BA stimulation of cell-surface TGR5on neurons may also modulate GLP-1secretion[61].In pe-ripheral tissues,TGR5activation may increase activation of the type2deiodinase,resulting in increased active thyroid hormone,mitochondrial oxidative capacity,and energy expenditure[2].A recent human genetic study demonstrates that a single nucleotide polymorphism(SNP)at the TGR5 locus(rs3731859)is associated with BMI,waist circumference,intramyocellular lipids,and fasting GLP-1levels[62].Furthermore,TGR5-null mice have a25%reduction in bile acid pool size,and female Tgr5 null mice show increased weight gain and fat accumulation when fed a high fat diet[63].Further support for the regulatory role of TGR5in glucose homeostasis comes from thefinding that TGR5 agonists decrease blood glucose in animals[64].Bile acids in humansIn healthy individuals,BA levelsfluctuate with cycles of fasting and refeeding.BA robustly increase in response to an oral glucose load[65].Such responses are increased in insulin sensitive individuals and are blunted in individuals with prediabetes[55],suggesting dysregulation of bile acid pools and/or intestinal regulation in insulin resistance.The majority of studies have analysed bile acid levels and species distribution in the fasting state; many of these demonstrate alterations in insulin resistance and diabetes.For example,one study demonstrated1.6-fold increases in deoxycholic acid(DCA)in T2D[66].Similarly,Haeusler et al. demonstrated that12a e hydroxylated species(sum of CA,DCA,and their conjugates)are significantly higher in patients with T2D[67].Furthermore,ratios of12-hydroxylated/non e12-hydroxylated BAs are associated with key features of IR,including higher insulin,glucose,and triglyceride(TG)levels and lower HDL cholesterol[67].Brufau and colleagues showed that individuals with T2D had higher cholic acid(CA)synthesis rates and enlarged DCA pool size[68].Our group recently reported that concen-trations of total taurine-conjugated BA were higher in T2D and intermediate in individuals with impaired glucose tolerance[69].Interestingly,total taurine-BA were positively associated with fasting and post-load glucose levels,fasting insulin,and HOMA-IR.However,insulin-mediated glycaemic improvement in T2D patients did not change fasting serum total BA,or BA composition,suggesting dysregulation of BA levels is not directly linked to glycaemic burden but possible due to other aspects of insulin resistance or the metabolic syndrome.Bile acids are increased following bariatric surgeryBariatric surgery is increasingly recognized as a robust method to not only reduce body weight,but also to reduce glycaemia and medication requirement(so called diabetes‘remission’)[70].Bariatric surgical procedures include Roux-en-Y gastric bypass(RYGB),vertical sleeve gastrectomy(VSG), laparoscopic adjustable gastric banding(LAGB)and biliopancreatic diversion(BPD).In this context,it is interesting that several studies have demonstrated that bile acids are markedly increased following bariatric surgery[5,6,71,72].Interestingly,total bile acids in post-bypass patients are correlated with improvement in several key metabolic parameters;bile acids are inversely correlated with post-prandial glucose,triglycerides,and positively correlated with adiponectin and peak GLP1levels following a mixed meal test.These intriguing data suggest increased serum bile acid levels could contribute to improvements in insulin sensitivity,incretin secretion,and postprandial glycaemia in response to bariatric surgery[6].Despite these intriguing data,it remains uncertain whether increased BA are absolutely essential for metabolic improvements following bariatric surgery,particularly during the early postoperative period.For example,longitudinal studies in humans demonstrate that increases in BA are not detecteduntil 1year postoperatively [73],despite improved glucose levels and reduced hepatic glucose output within one week of surgery [74,75].By contrast,increases in both fasting and postprandial BA are also observed as early as 14days following VSG in rodents [76,77].In addition,both RYGB and VSG can alter the distribution of bile acid species [8][78].By contrast,circulating BA do not change signi ficantly after LAGB [4,73,79],and could contribute to reduced ef ficacy of this procedure for long-term resolution of T2D as compared with RYGB or VSG.Importantly,increased BA action,via FXR-mediated effects on both gut microbiome and transcriptional pathways,appears to be required to achieve the metabolic effects of surgery,at least in rodent models [77].Intriguingly,direct modulation of small intestinal anatomy can alter bile acid levels and composi-tion.Mid-to-distal small intestinal resection,with preservation of the terminal ileum,increases bile acid levels [80].Similarly,interposition of the ileum into more proximal segments of gut also increases bile acid levels [81].Nonsurgical approaches may also be effective;for example,endoluminal sleeves,which allow luminal contents to bypass the duodenal mucosa,also increase bile acids in rodents and improve glucose metabolism [82].While there are many unanswered questions,these data suggest that modulation of segmental intestinal anatomy,and/or changes in intestinal flora which result from these modi fications,may improve systemic metabolism via BA-dependent mechanisms.Modulating bile acids as a potential therapeutic approach for obesity and T2DThe close links between plasma levels of bile acids and a host of key metabolic parameters raise the possibility that modulation of BA could be used as a therapeutic approach for the treatment of metabolic diseases.Dietary supplementation with cholic acid (CA)increases energy expenditure,reducing weight gain during high-fat feeding [83].While the precise mechanism remains uncertain,BA increase expression and activity of the type 2iodothyronine deiodinase (D2)via a TGR5-cAMP-mediated pathway,thus increasing active thyroid hormone (T3)availability and energy expenditure in tissues critical for thermogenesis,such as BAT [10].Similarly,CDCA has been shown to increase energy expenditure by induction of UCP1and activation of thermogenesis in BAT in mice [84].Bile acid sequestrants,which increase the CA pool size (while reducing CDCA and DCA pools),also reduce glucose,hemoglobin A1c,and cholesterol levels in patients with type 2diabetes [85e 87].Thus,therapeutic strategies which increase circulating BA levels or modulate relative distribution of active bile acid species could be an effective approach to improving systemic metabolism.Bile acid-binding resinsBile acid binding resins (BABR)(cholestyramine,colestipol,colestimide,and colesevelam)are positively charged nondigestible resins that bind to bile acids in the intestine to form an insoluble complex that is excreted in the feces.BABR have been successfully employed for the treatment of hypercholesterolaemia for many years.Recently,the second-generation BABR colestimide and cole-sevelam were found to improve glycaemic control in patients with T2D [86,88e 91].Several possible mechanisms have been proposed for these effects.BABR not only increase plasma BA but also change the composition of the BA pool [92].These changes in BA may promote increased energy expenditure,as observed in rodents [93].In addition,BABRs stimulate the expression of proglucagon and release of GLP1,thus improving incretin-mediated insulin secretion and reducing plasma glucose [94].This effect of colesevelam was achieved through regulation of FXR/FGF19and TGR5/GLP-1signalling pathways[89].Colestimide also decreases postprandial plasma glucose and increases GLP-1secretion in patients with T2D [85].Despite these intriguing possibilities,there is not a clear relationship between BA metabolism and improvements in glycaemia,and changes in FGF19or energy expenditure are not consistently observed in human studies [68,95].Nevertheless,BA sequestrants regulate glucose ho-meostasis,potentially at least in part by modulating FXR-and TGR5-mediated pathways.FXR agonistsSince FXR modulates many of the metabolic effects of bile acids,activation of FXR could be another approach to treat metabolic disease [96].Treatment with the FXR ligand GW4064signi ficantlyH.Ma,M.E.Patti /Best Practice &Research Clinical Gastroenterology 28(2014)573e 583578H.Ma,M.E.Patti/Best Practice&Research Clinical Gastroenterology28(2014)573e583579 decreases plasma glucose,triglycerides,and cholesterol in both wild-type and diabetic db/db mice [50].6-ECDCA,another FXR agonist,can decrease glucose,cholesterol,free fatty acid,and triglyceride levels in Zucker fa/fa rats[54]by enhancing glucose disposal,reducing body weight,in parallel with reduced expression of PEPCK and glucose-6-phosphates(G6Pase)in ob/ob mice.Interestingly,these effects of FXR agonists are achieved despite decreased bile acid levels,largely through direct activation of hepatic FXR-SHP and intestinal FXR-FGF15/19pathways[96].These data again highlight the importance of FXR pathways in mediating metabolic effects of BA.TGR5agonistsThe cell surface receptor TGR5represents another novel pharmacological target for the treat-ment of the metabolic syndrome and related disorders[97,98].TGR5can be activated by either synthetic ligands[10,80],or by BA in a dose-dependent manner,with potency of activation depending on specific BA species:lithocholic acid>deoxycholic acid>chenodeoxycholic acid >cholic acid.In rodents,synthetic TGR5agonists decrease plasma glucose and insulin levels and protect against weight gain induced by a high-fat diet[64].The expression and activity of the type2 deiodinase and energy expenditure can be increased with incubation of skeletal muscle with a synthetic TGR5agonist[10].Therapeutic modulation of BA via manipulation of the intestinal tract and its residentflora As noted above,bariatric surgery is associated with increased plasma BA levels and alterated composition of BA species.In turn,increased BA may contribute to enhanced FXR and TGR5acti-vation,leading to reduced hepatic glucose production,increased GLP1secretion,and increased systemic energy expenditure.In support of this concept,recent data implicate FXR activity as a critical mediator of the beneficial effects of bariatric surgery in rodents[85].Given the important role of the gut microbiome in modulating bile acid pool size,composition,and enterohepatic recirculation,it is intriguing to consider whether modification of the gut microbiome could pro-mote BA-mediated beneficial changes in metabolism.This could potentially be achieved by altered dietary fatty acid composition[99]or with probiotics which modulate gutflora[100,101].For example,one recent study demonstrated that probiotics could increase BA deconjugation,increase fecal BA excretion,and increase hepatic BA synthesis in an FGF-dependent mechanism[101].These intriguing data provide hope that BA action on the gut microbiome and systemic metabolism could be harnessed to yield beneficial effects similar to those observed after bariatric surgery,but in the absence of invasive surgery.This line of investigation will be an important question for future studies.SummaryTaken together,data from both humans and preclinical animal models demonstrate that BA are important signalling molecules which contribute to regulation of whole-body glucose and lipid metabolism and body weight.Such effects of BA are largely mediated by the nuclear receptor FXR and the G protein-coupled receptor TGR5.Future research employing proteomic,metabolomic,and lip-idomic approaches are likely to help in identifying bile acid-related biomarkers which may be useful for predicting and assessing response to BA-related therapy for human obesity and metabolic syn-drome.Moreover,novel approaches to altering biliaryflow and enterohepatic recirculation,plasma BA levels,composition of BA pools,and downstream effectors of BA signalling pathways should be pur-sued,as they may be effective strategies for the management of obesity,insulin resistance,type2 diabetes,and other components of the metabolic syndrome.Conflict of interestNone.AcknowledgementsThe authors gratefully acknowledge grant support from Hebei Health Department of Scienti fic Research Fund (to HM),P30DK036836DRC (Joslin Diabetes Center),and the American Diabetes As-sociation (to MEP).References[1]Houten SM,Watanabe M,Auwerx J.Endocrine functions of bile acids.EMBO J 2006;25:1419e 25.[2]Watanabe M,Houten SM,Mataki C,Christoffolete MA,Kim BW,Sato H,et al.Bile acids induce energy expenditure bypromoting intracellular thyroid hormone activation.Nature 2006;439:484e 9.[3]Chiang JY.Bile acid metabolism and pr Physiol 2013;3:1191e 212.[4]Kohli R,Bradley D,Setchell KD,Eagon JC,Abumrad N,Klein S.Weight loss induced by Roux-en-Y gastric bypass but notlaparoscopic adjustable gastric banding increases circulating bile acids.J Clin Endocrinol Metab 2013;98:E708e 12.[5]Simonen M,Dali-Youcef N,Kaminska D,Venesmaa S,Kakela P,Paakkonen M,et al.Conjugated bile acids associate withaltered rates of glucose and lipid oxidation after Roux-en-Y gastric bypass.Obes Surg 2012;22:1473e 80.[6]Patti ME,Houten SM,Bianco AC,Bernier R,Larsen PR,Holst JJ,et al.Serum bile acids are higher in humans with priorgastric bypass:potential contribution to improved glucose and lipid metabolism.Obesity 2009;17:1671e 7.[7]Chiang JY.Bile acids:regulation of synthesis.J Lipid Res 2009;50:1955e 66.[8]Chiang JY.Regulation of bile acid synthesis.Front Biosci 1998;3:d176e 93.[9]Deo AK,Bandiera SM.Biotransformation of lithocholic acid by rat hepatic microsomes:metabolite analysis by liquidchromatography/mass spectrometry.Drug Metab Dispos 2008;36:442e 51.[10]Russell DW.Fifty years of advances in bile acid synthesis and metabolism.J Lipid Res 2009;(Suppl.50):S120e 5.[11]Hofmann AF,Hagey LR.Bile acids:chemistry,pathochemistry,biology,pathobiology,and therapeutics.Cellular andmolecular life sciences.CMLS 2008;65:2461e 83.[12]Sayin SI,Wahlstrom A,Felin J,Jantti S,Marschall HU,Bamberg K,et al.Gut microbiota regulates bile acid metabolism byreducing the levels of tauro-beta-muricholic acid,a naturally occurring FXR antagonist.Cell Metab 2013;17:225e 35.[13]Moschetta A,Xu F,Hagey LR,van Berge-Henegouwen GP,van Erpecum KJ,Brouwers JF,et al.A phylogenetic survey ofbiliary lipids in vertebrates.J lipid Res 2005;46:2221e 32.[14]Hofmann AF,Borgstroem B.The intraluminal phase of fat digestion in man:the lipid content of the micellar and oilphases of intestinal content obtained during fat digestion and absorption.J Clin Invest 1964;43:247e 57.H.Ma,M.E.Patti /Best Practice &Research Clinical Gastroenterology 28(2014)573e 583580。

2021⁃04⁃10计算机应用,Journal of Computer Applications2021,41(4):1012-1019ISSN 1001⁃9081CODEN JYIIDU http ：//基于注意力融合网络的视频超分辨率重建卞鹏程，郑忠龙*，李明禄，何依然，王天翔，张大伟，陈丽媛（浙江师范大学数学与计算机科学学院，浙江金华321004）（∗通信作者电子邮箱zhonglong@ ）摘要：基于深度学习的视频超分辨率方法主要关注视频帧内和帧间的时空关系，但以往的方法在视频帧的特征对齐和融合方面存在运动信息估计不精确、特征融合不充分等问题。

针对这些问题，采用反向投影原理并结合多种注意力机制和融合策略构建了一个基于注意力融合网络（AFN ）的视频超分辨率模型。

首先，在特征提取阶段，为了处理相邻帧和参考帧之间的多种运动，采用反向投影结构来获取运动信息的误差反馈；然后，使用时间、空间和通道注意力融合模块来进行多维度的特征挖掘和融合；最后，在重建阶段，将得到的高维特征经过卷积重建出高分辨率的视频帧。

通过学习视频帧内和帧间特征的不同权重，充分挖掘了视频帧之间的相关关系，并利用迭代网络结构采取渐进的方式由粗到精地处理提取到的特征。

在两个公开的基准数据集上的实验结果表明，AFN 能够有效处理包含多种运动和遮挡的视频，与一些主流方法相比在量化指标上提升较大，如对于4倍重建任务，AFN 产生的视频帧的峰值信噪比（PSNR ）在Vid4数据集上比帧循环视频超分辨率网络（FRVSR ）产生的视频帧的PSNR 提高了13.2%，在SPMCS 数据集上比动态上采样滤波视频超分辨率网络（VSR -DUF ）产生的视频帧的PSNR 提高了15.3%。

关键词：超分辨率；注意力机制；特征融合；反向投影；视频重建中图分类号：TP391.4文献标志码：AAttention fusion network based video super -resolution reconstructionBIAN Pengcheng ，ZHENG Zhonglong *，LI Minglu ，HE Yiran ，WANG Tianxiang ，ZHANG Dawei ，CHEN Liyuan（College of Mathematics and Computer Science ，Zhejiang Normal University ，Jinhua Zhejiang 321004，China ）Abstract:Video super -resolution methods based on deep learning mainly focus on the inter -frame and intra -frame spatio -temporal relationships in the video ，but previous methods have many shortcomings in the feature alignment and fusion of video frames ，such as inaccurate motion information estimation and insufficient feature fusion.Aiming at these problems ，a video super -resolution model based on Attention Fusion Network （AFN ）was constructed with the use of the back -projection principle and the combination of multiple attention mechanisms and fusion strategies.Firstly ，at the feature extraction stage ，in order to deal with multiple motions between neighbor frames and reference frame ，the back -projection architecture was used to obtain the error feedback of motion information.Then ，a temporal ，spatial and channel attention fusion module was used to perform the multi -dimensional feature mining and fusion.Finally ，at the reconstruction stage ，the obtained high -dimensional features were convoluted to reconstruct high -resolution video frames.By learning different weights of features within and between video frames ，the correlations between video frames were fully explored ，and an iterative network structure was adopted to process the extracted features gradually from coarse to fine.Experimental results on two public benchmark datasets show that AFN can effectively process videos with multiple motions and occlusions ，and achieves significant improvements in quantitative indicators compared to some mainstream methods.For instance ，for 4-times reconstruction task ，the Peak Signal -to -Noise Ratio （PSNR ）of the frame reconstructed by AFN is 13.2%higher than that of Frame Recurrent Video Super -Resolution network （FRVSR ）on Vid4dataset and 15.3%higher than that of Video Super -Resolution network using Dynamic Upsampling Filter （VSR -DUF ）on SPMCS dataset.Key words:super -resolution;attention mechanism;feature fusion;back -projection;video reconstruction文章编号：1001-9081（2021）04-1012-08DOI ：10.11772/j.issn.1001-9081.2020081292收稿日期：2020⁃08⁃24；修回日期：2020⁃09⁃18；录用日期：2020⁃10⁃13。

Secrets of Optical Flow Estimation and Their PrinciplesDeqing Sun Brown UniversityStefan RothTU DarmstadtMichael J.BlackBrown UniversityAbstractThe accuracy of opticalflow estimation algorithms has been improving steadily as evidenced by results on the Middlebury opticalflow benchmark.The typical formula-tion,however,has changed little since the work of Horn and Schunck.We attempt to uncover what has made re-cent advances possible through a thorough analysis of how the objective function,the optimization method,and mod-ern implementation practices influence accuracy.We dis-cover that“classical”flow formulations perform surpris-ingly well when combined with modern optimization and implementation techniques.Moreover,wefind that while medianfiltering of intermediateflowfields during optimiza-tion is a key to recent performance gains,it leads to higher energy solutions.To understand the principles behind this phenomenon,we derive a new objective that formalizes the medianfiltering heuristic.This objective includes a non-local term that robustly integratesflow estimates over large spatial neighborhoods.By modifying this new term to in-clude information aboutflow and image boundaries we de-velop a method that ranks at the top of the Middlebury benchmark.1.IntroductionThefield of opticalflow estimation is making steady progress as evidenced by the increasing accuracy of cur-rent methods on the Middlebury opticalflow benchmark [6].After nearly30years of research,these methods have obtained an impressive level of reliability and accuracy [33,34,35,40].But what has led to this progress?The majority of today’s methods strongly resemble the original formulation of Horn and Schunck(HS)[18].They combine a data term that assumes constancy of some image property with a spatial term that models how theflow is expected to vary across the image.An objective function combin-ing these two terms is then optimized.Given that this basic structure is unchanged since HS,what has enabled the per-formance gains of modern approaches?The paper has three parts.In thefirst,we perform an ex-tensive study of current opticalflow methods and models.The most accurate methods on the Middleburyflow dataset make different choices about how to model the objective function,how to approximate this model to make it com-putationally tractable,and how to optimize it.Since most published methods change all of these properties at once, it can be difficult to know which choices are most impor-tant.To address this,we define a baseline algorithm that is“classical”,in that it is a direct descendant of the original HS formulation,and then systematically vary the model and method using different techniques from the art.The results are surprising.Wefind that only a small number of key choices produce statistically significant improvements and that they can be combined into a very simple method that achieves accuracies near the state of the art.More impor-tantly,our analysis reveals what makes currentflow meth-ods work so well.Part two examines the principles behind this success.We find that one algorithmic choice produces the most signifi-cant improvements:applying a medianfilter to intermedi-ateflow values during incremental estimation and warping [33,34].While this heuristic improves the accuracy of the recoveredflowfields,it actually increases the energy of the objective function.This suggests that what is being opti-mized is actually a new and different ing ob-servations about medianfiltering and L1energy minimiza-tion from Li and Osher[23],we formulate a new non-local term that is added to the original,classical objective.This new term goes beyond standard local(pairwise)smoothness to robustly integrate information over large spatial neigh-borhoods.We show that minimizing this new energy ap-proximates the original optimization with the heuristic me-dianfiltering step.Note,however,that the new objective falls outside our definition of classical methods.Finally,once the medianfiltering heuristic is formulated as a non-local term in the objective,we immediately recog-nize how to modify and improve it.In part three we show how information about image structure andflow boundaries can be incorporated into a weighted version of the non-local term to prevent over-smoothing across boundaries.By in-corporating structure from the image,this weighted version does not suffer from some of the errors produced by median filtering.At the time of publication(March2010),the re-sulting approach is ranked1st in both angular and end-point errors in the Middlebury evaluation.In summary,the contributions of this paper are to(1)an-alyze currentflow models and methods to understand which design choices matter;(2)formulate and compare several classical objectives descended from HS using modern meth-ods;(3)formalize one of the key heuristics and derive a new objective function that includes a non-local term;(4)mod-ify this new objective to produce a state-of-the-art method. In doing this,we provide a“recipe”for others studying op-ticalflow that can guide their design choices.Finally,to en-able comparison and further innovation,we provide a public M ATLAB implementation[1].2.Previous WorkIt is important to separately analyze the contributions of the objective function that defines the problem(the model) and the optimization algorithm and implementation used to minimize it(the method).The HS formulation,for example, has long been thought to be highly inaccurate.Barron et al.[7]reported an average angular error(AAE)of~30degrees on the“Yosemite”sequence.This confounds the objective function with the particular optimization method proposed by Horn and Schunck1.When optimized with today’s meth-ods,the HS objective achieves surprisingly competitive re-sults despite the expected over-smoothing and sensitivity to outliers.Models:The global formulation of opticalflow intro-duced by Horn and Schunck[18]relies on both brightness constancy and spatial smoothness assumptions,but suffers from the fact that the quadratic formulation is not robust to outliers.Black and Anandan[10]addressed this by re-placing the quadratic error function with a robust formula-tion.Subsequently,many different robust functions have been explored[12,22,31]and it remains unclear which is best.We refer to all these spatially-discrete formulations derived from HS as“classical.”We systematically explore variations in the formulation and optimization of these ap-proaches.The surprise is that the classical model,appropri-ately implemented,remains very competitive.There are many formulations beyond the classical ones that we do not consider here.Significant ones use oriented smoothness[25,31,33,40],rigidity constraints[32,33], or image segmentation[9,21,41,37].While they deserve similar careful consideration,we expect many of our con-clusions to carry forward.Note that one can select among a set of models for a given sequence[4],instead offinding a “best”model for all the sequences.Methods:Many of the implementation details that are thought to be important date back to the early days of op-1They noted that the correct way to optimize their objective is by solv-ing a system of linear equations as is common today.This was impractical on the computers of the day so they used a heuristic method.ticalflow.Current best practices include coarse-to-fine es-timation to deal with large motions[8,13],texture decom-position[32,34]or high-orderfilter constancy[3,12,16, 22,40]to reduce the influence of lighting changes,bicubic interpolation-based warping[22,34],temporal averaging of image derivatives[17,34],graduated non-convexity[11]to minimize non-convex energies[10,31],and medianfilter-ing after each incremental estimation step to remove outliers [34].This medianfiltering heuristic is of particular interest as it makes non-robust methods more robust and improves the accuracy of all methods we tested.The effect on the objec-tive function and the underlying reason for its success have not previously been analyzed.Least median squares estima-tion can be used to robustly reject outliers inflow estimation [5],but previous work has focused on the data term.Related to medianfiltering,and our new non-local term, is the use of bilateralfiltering to prevent smoothing across motion boundaries[36].The approach separates a varia-tional method into twofiltering update stages,and replaces the original anisotropic diffusion process with multi-cue driven bilateralfiltering.As with medianfiltering,the bi-lateralfiltering step changes the original energy function.Models that are formulated with an L1robust penalty are often coupled with specialized total variation(TV)op-timization methods[39].Here we focus on generic opti-mization methods that can apply to any model andfind they perform as well as reported results for specialized methods.Despite recent algorithmic advances,there is a lack of publicly available,easy to use,and accurateflow estimation software.The GPU4Vision project[2]has made a substan-tial effort to change this and provides executablefiles for several accurate methods[32,33,34,35].The dependence on the GPU and the lack of source code are limitations.We hope that our public M ATLAB code will not only help in un-derstanding the“secrets”of opticalflow,but also let others exploit opticalflow as a useful tool in computer vision and relatedfields.3.Classical ModelsWe write the“classical”opticalflow objective function in its spatially discrete form asE(u,v)=∑i,j{ρD(I1(i,j)−I2(i+u i,j,j+v i,j))(1)+λ[ρS(u i,j−u i+1,j)+ρS(u i,j−u i,j+1)+ρS(v i,j−v i+1,j)+ρS(v i,j−v i,j+1)]}, where u and v are the horizontal and vertical components of the opticalflowfield to be estimated from images I1and I2,λis a regularization parameter,andρD andρS are the data and spatial penalty functions.We consider three different penalty functions:(1)the quadratic HS penaltyρ(x)=x2;(2)the Charbonnier penaltyρ(x)=√x2+ 2[13],a dif-ferentiable variant of the L1norm,the most robust convexfunction;and(3)the Lorentzianρ(x)=log(1+x22σ2),whichis a non-convex robust penalty used in[10].Note that this classical model is related to a standard pairwise Markov randomfield(MRF)based on a4-neighborhood.In the remainder of this section we define a baseline method using several techniques from the literature.This is not the“best”method,but includes modern techniques and will be used for comparison.We only briefly describe the main choices,which are explored in more detail in the following section and the cited references,especially[30].Quantitative results are presented throughout the remain-der of the text.In all cases we report the average end-point error(EPE)on the Middlebury training and test sets,de-pending on the experiment.Given the extensive nature of the evaluation,only average results are presented in the main body,while the details for each individual sequence are given in[30].3.1.Baseline methodsTo gain robustness against lighting changes,we follow [34]and apply the Rudin-Osher-Fatemi(ROF)structure texture decomposition method[28]to pre-process the in-put sequences and linearly combine the texture and struc-ture components(in the proportion20:1).The parameters are set according to[34].Optimization is performed using a standard incremental multi-resolution technique(e.g.[10,13])to estimateflow fields with large displacements.The opticalflow estimated at a coarse level is used to warp the second image toward thefirst at the nextfiner level,and aflow increment is cal-culated between thefirst image and the warped second im-age.The standard deviation of the Gaussian anti-aliasingfilter is set to be1√2d ,where d denotes the downsamplingfactor.Each level is recursively downsampled from its near-est lower level.In building the pyramid,the downsampling factor is not critical as pointed out in the next section and here we use the settings in[31],which uses a factor of0.8 in thefinal stages of the optimization.We adaptively de-termine the number of pyramid levels so that the top level has a width or height of around20to30pixels.At each pyramid level,we perform10warping steps to compute the flow increment.At each warping step,we linearize the data term,whichinvolves computing terms of the type∂∂x I2(i+u k i,j,j+v k i,j),where∂/∂x denotes the partial derivative in the horizon-tal direction,u k and v k denote the currentflow estimate at iteration k.As suggested in[34],we compute the deriva-tives of the second image using the5-point derivativefilter1 12[−180−81],and warp the second image and its deriva-tives toward thefirst using the currentflow estimate by bicu-bic interpolation.We then compute the spatial derivatives ofAvg.Rank Avg.EPEClassic-C14.90.408HS24.60.501Classic-L19.80.530HS[31]35.10.872BA(Classic-L)[31]30.90.746Adaptive[33]11.50.401Complementary OF[40]10.10.485Table1.Models.Average rank and end-point error(EPE)on the Middlebury test set using different penalty functions.Two current methods are included for comparison.thefirst image,average with the warped derivatives of the second image(c.f.[17]),and use this in place of∂I2∂x.For pixels moving out of the image boundaries,we set both their corresponding temporal and spatial derivatives to zero.Af-ter each warping step,we apply a5×5medianfilter to the newly computedflowfield to remove outliers[34].For the Charbonnier(Classic-C)and Lorentzian (Classic-L)penalty function,we use a graduated non-convexity(GNC)scheme[11]as described in[31]that lin-early combines a quadratic objective with a robust objective in varying proportions,from fully quadratic to fully robust. Unlike[31],a single regularization weightλis used for both the quadratic and the robust objective functions.3.2.Baseline resultsThe regularization parameterλis selected among a set of candidate values to achieve the best average end-point error (EPE)on the Middlebury training set.For the Charbonnier penalty function,the candidate set is[1,3,5,8,10]and 5is optimal.The Charbonnier penalty uses =0.001for both the data and the spatial term in Eq.(1).The Lorentzian usesσ=1.5for the data term,andσ=0.03for the spa-tial term.These parameters arefixed throughout the exper-iments,except where mentioned.Table1summarizes the EPE results of the basic model with three different penalty functions on the Middlebury test set,along with the two top performers at the time of publication(considering only published papers).The clas-sic formulations with two non-quadratic penalty functions (Classic-C)and(Classic-L)achieve competitive results de-spite their simplicity.The baseline optimization of HS and BA(Classic-L)results in significantly better accuracy than previously reported for these models[31].Note that the analysis also holds for the training set(Table2).At the time of publication,Classic-C ranks13th in av-erage EPE and15th in AAE in the Middlebury benchmark despite its simplicity,and it serves as the baseline below.It is worth noting that the spatially discrete MRF formulation taken here is competitive with variational methods such as [33].Moreover,our baseline implementation of HS has a lower average EPE than many more sophisticated methods.Avg.EPE significance p-value Classic-C0.298——HS0.38410.0078Classic-L0.31910.0078Classic-C-brightness0.28800.9453HS-brightness0.38710.0078Classic-L-brightness0.32500.2969Gradient0.30500.4609Table2.Pre-Processing.Average end-point error(EPE)on the Middlebury training set for the baseline method(Classic-C)using different pre-processing techniques.Significance is always with respect to Classic-C.4.Secrets ExploredWe evaluate a range of variations from the baseline ap-proach that have appeared in the literature,in order to illu-minate which may be of importance.This analysis is per-formed on the Middlebury training set by changing only one property at a time.Statistical significance is determined using a Wilcoxon signed rank test between each modified method and the baseline Classic-C;a p value less than0.05 indicates a significant difference.Pre-Processing.For each method,we optimize the regu-larization parameterλfor the training sequences and report the results in Table2.The baseline uses a non-linear pre-filtering of the images to reduce the influence of illumina-tion changes[34].Table2shows the effect of removing this and using a standard brightness constancy model(*-brightness).Classic-C-brightness actually achieves lower EPE on the training set than Classic-C but significantly lower accuracy on the test set:Classic-C-brightness= 0.726,HS-brightness=0.759,and Classic-L-brightness =0.603–see Table1for comparison.This disparity sug-gests overfitting is more severe for the brightness constancy assumption.Gradient only imposes constancy of the gra-dient vector at each pixel as proposed in[12](i.e.it robustly penalizes Euclidean distance between image gradients)and has similar performance in both training and test sets(c.f. Table8).See[30]for results of more alternatives. Secrets:Some form of imagefiltering is useful but simple derivative constancy is nearly as good as the more sophisti-cated texture decomposition method.Coarse-to-fine estimation and GNC.We vary the number of warping steps per pyramid level andfind that3warping steps gives similar results as using10(Table3).For the GNC scheme,[31]uses a downsampling factor of0.8for non-convex optimization.A downsampling factor of0.5 (Down-0.5),however,has nearly identical performance Removing the GNC step for the Charbonnier penalty function(w/o GNC)results in higher EPE on most se-quences and higher energy on all sequences(Table4).This suggests that the GNC method is helpful even for the con-vex Charbonnier penalty function due to the nonlinearity ofAvg.EPE significance p-value Classic-C0.298——3warping steps0.30400.9688Down-0.50.2980 1.0000w/o GNC0.35400.1094Bilinear0.30200.1016w/o TA VG0.30600.1562Central derivativefilter0.30000.72667-point derivativefilter[13]0.30200.3125Bicubic-II0.29010.0391GC-0.45(λ=3)0.29210.0156GC-0.25(λ=0.7)0.2980 1.0000MF3×30.30500.1016MF7×70.30500.56252×MF0.3000 1.00005×MF0.30500.6875w/o MF0.35210.0078Classic++0.28510.0078 Table3.Model and Methods.Average end-point error(EPE)on the Middlebury training set for the baseline method(Classic-C) using different algorithm and modelingchoices.Figure1.Different penalty functions for the spatial terms:Char-bonnier( =0.001),generalized Charbonnier(a=0.45and a=0.25),and Lorentzian(σ=0.03).the data term.Secrets:The downsampling factor does not matter when using a convex penalty;a standard factor of0.5isfine. Some form of GNC is useful even for a convex robust penalty like Charbonnier because of the nonlinear data term. Interpolation method and derivatives.Wefind that bicu-bic interpolation is more accurate than bilinear(Table3, Bilinear),as already reported in previous work[34].Re-moving temporal averaging of the gradients(w/o TA VG), using Central differencefilters,or using a7-point deriva-tivefilter[13]all reduce accuracy compared to the base-line,but not significantly.The M ATLAB built-in function interp2is based on cubic convolution approximation[20]. The spline-based interpolation scheme[26]is consistently better(Bicubic-II).See[30]for more discussions. Secrets:Use spline-based bicubic interpolation with a5-pointfilter.Temporal averaging of the derivatives is proba-bly worthwhile for a small computational expense. Penalty functions.Wefind that the convex Charbonnier penalty performs better than the more robust,non-convex Lorentzian on both the training and test sets.One reason might be that non-convex functions are more difficult to op-timize,causing the optimization scheme tofind a poor local(a)With medianfiltering(b)Without medianfilteringFigure2.Estimatedflowfields on sequence“RubberWhale”using Classic-C with and without(w/o MF)the medianfiltering step. Color coding as in[6].(a)(w/MF)energy502,387and(b)(w/o MF)energy449,290.The medianfiltering step helps reach a so-lution free from outliers but with a higher energy.optimum.We investigate a generalized Charbonnier penalty functionρ(x)=(x2+ 2)a that is equal to the Charbon-nier penalty when a=0.5,and non-convex when a<0.5 (see Figure1).We optimize the regularization parameterλagain.Wefind a slightly non-convex penalty with a=0.45 (GC-0.45)performs consistently better than the Charbon-nier penalty,whereas more non-convex penalties(GC-0.25 with a=0.25)show no improvement.Secrets:The less-robust Charbonnier is preferable to the Lorentzian and a slightly non-convex penalty function(GC-0.45)is better still.Medianfiltering.The baseline5×5medianfilter(MF 5×5)is better than both MF3×3[34]and MF7×7but the difference is not significant(Table3).When we perform5×5medianfiltering twice(2×MF)orfive times(5×MF)per warping step,the results are worse.Finally,removing the medianfiltering step(w/o MF)makes the computedflow significantly less accurate with larger outliers as shown in Table3and Figure2.Secrets:Medianfiltering the intermediateflow results once after every warping iteration is the single most important secret;5×5is a goodfilter size.4.1.Best PracticesCombining the analysis above into a single approach means modifying the baseline to use the slightly non-convex generalized Charbonnier and the spline-based bicu-bic interpolation.This leads to a statistically significant improvement over the baseline(Table3,Classic++).This method is directly descended from HS and BA,yet updated with the current best optimization practices known to us. This simple method ranks9th in EPE and12th in AAE on the Middlebury test set.5.Models Underlying Median FilteringOur analysis reveals the practical importance of median filtering during optimization to denoise theflowfield.We ask whether there is a principle underlying this heuristic?One interesting observation is thatflowfields obtained with medianfiltering have substantially higher energy than those without(Table4and Figure2).If the medianfilter is helping to optimize the objective,it should lead to lower energies.Higher energies and more accurate estimates sug-gest that incorporating medianfiltering changes the objec-tive function being optimized.The insight that follows from this is that the medianfil-tering heuristic is related to the minimization of an objective function that differs from the classical one.In particular the optimization of Eq.(1),with interleaved medianfiltering, approximately minimizesE A(u,v,ˆu,ˆv)=(2)∑i,j{ρD(I1(i,j)−I2(i+u i,j,j+v i,j))+λ[ρS(u i,j−u i+1,j)+ρS(u i,j−u i,j+1)+ρS(v i,j−v i+1,j)+ρS(v i,j−v i,j+1)]}+λ2(||u−ˆu||2+||v−ˆv||2)+∑i,j∑(i ,j )∈N i,jλ3(|ˆu i,j−ˆu i ,j |+|ˆv i,j−ˆv i ,j |),whereˆu andˆv denote an auxiliaryflowfield,N i,j is the set of neighbors of pixel(i,j)in a possibly large area andλ2 andλ3are scalar weights.The term in braces is the same as theflow energy from Eq.(1),while the last term is new. This non-local term[14,15]imposes a particular smooth-ness assumption within a specified region of the auxiliary flowfieldˆu,ˆv2.Here we take this term to be a5×5rectan-gular region to match the size of the medianfilter in Classic-C.A third(coupling)term encouragesˆu,ˆv and u,v to be the same(c.f.[33,39]).The connection to medianfiltering(as a denoising method)derives from the fact that there is a direct relation-ship between the median and L1minimization.Consider a simplified version of Eq.(2)with just the coupling and non-local terms,where E(ˆu)=λ2||u−ˆu||2+∑i,j∑(i ,j )∈N i,jλ3|ˆu i,j−ˆu i ,j |.(3)While minimizing this is similar to medianfiltering u,there are two differences.First,the non-local term minimizes the L1distance between the central value and allflow values in its neighborhood except itself.Second,Eq.(3)incorpo-rates information about the data term through the coupling equation;medianfiltering theflow ignores the data term.The formal connection between Eq.(3)and medianfil-tering3is provided by Li and Osher[23]who show that min-2Bruhn et al.[13]also integrated information over a local region in a global method but did so for the data term.3Hsiao et al.[19]established the connection in a slightly different way.Classic-C 0.5890.7480.8660.502 1.816 2.317 1.126 1.424w/o GNC 0.5930.7500.8700.506 1.845 2.518 1.142 1.465w/o MF0.5170.7010.6680.449 1.418 1.830 1.066 1.395Table 4.Eq.(1)energy (×106)for the optical flow fields computed on the Middlebury training set .Note that Classic-C uses graduated non-convexity (GNC),which reduces the energy,and median filtering,which increases it.imizing Eq.(3)is related to a different median computationˆu (k +1)i,j=median (Neighbors (k )∪Data)(4)where Neighbors (k )={ˆu (k )i ,j }for (i ,j )∈N i,j and ˆu (0)=u as well as Data ={u i,j ,u i,j ±λ3λ2,u i,j±2λ3λ2···,u i,j ±|N i,j |λ32λ2},where |N i,j |denotes the (even)number of neighbors of (i,j ).Note that the set of “data”values is balanced with an equal number of elements on either side of the value u i,j and that information about the data term is included through u i,j .Repeated application of Eq.(4)converges rapidly [23].Observe that,as λ3/λ2increases,the weighted data val-ues on either side of u i,j move away from the values of Neighbors and cancel each other out.As this happens,Eq.(4)approximates the median at the first iterationˆu (1)i,j ≈median (Neighbors (0)∪{u i,j }).(5)Eq.(2)thus combines the original objective with an ap-proximation to the median,the influence of which is con-trolled by λ3/λ2.Note in practice the weight λ2on thecoupling term is usually small or is steadily increased from small values [34,39].We optimize the new objective (2)by alternately minimizingE O (u ,v )=∑i,jρD (I 1(i,j )−I 2(i +u i,j ,j +v i,j ))+λ[ρS (u i,j −u i +1,j )+ρS (u i,j −u i,j +1)+ρS (v i,j −v i +1,j )+ρS (v i,j −v i,j +1)]+λ2(||u −ˆu ||2+||v −ˆv ||2)(6)andE M (ˆu ,ˆv )=λ2(||u −ˆu ||2+||v −ˆv ||2)(7)+∑i,j ∑(i ,j )∈N i,jλ3(|ˆu i,j −ˆu i ,j |+|ˆv i,j −ˆv i ,j |).Note that an alternative formulation would drop the cou-pling term and impose the non-local term directly on u and v .We find that optimization of the coupled set of equations is superior in terms of EPE performance.The alternating optimization strategy first holds ˆu ,ˆv fixed and minimizes Eq.(6)w.r.t.u ,v .Then,with u ,v fixed,we minimize Eq.(7)w.r.t.ˆu ,ˆv .Note that Eqs.(3)andAvg.EPE significancep -value Classic-C0.298——Classic-C-A0.30500.8125Table 5.Average end-point error (EPE)on the Middlebury train-ing set is shown for the new model with alternating optimization (Classic-C-A ).(7)can be minimized by repeated application of Eq.(4);weuse this approach with 5iterations.We perform 10steps of alternating optimizations at every pyramid level and change λ2logarithmically from 10−4to 102.During the first and second GNC stages,we set u ,v to be ˆu ,ˆv after every warp-ing step (this step helps reach solutions with lower energy and EPE [30]).In the end,we take ˆu ,ˆv as the final flow field estimate.The other parameters are λ=5,λ3=1.Alternatingly optimizing this new objective function (Classic-C-A )leads to similar results as the baseline Classic-C (Table 5).We also compare the energy of these solutions using the new objective and find the alternat-ing optimization produces the lowest energy solutions,as shown in Table 6.To do so,we set both the flow field u ,v and the auxiliary flow field ˆu ,ˆv to be the same in Eq.(2).In summary,we show that the heuristic median filter-ing step in Classic-C can now be viewed as energy min-imization of a new objective with a non-local term.The explicit formulation emphasizes the value of robustly inte-grating information over large neighborhoods and enables the improved model described below.6.Improved ModelBy formalizing the median filtering heuristic as an ex-plicit objective function,we can find ways to improve it.While median filtering in a large neighborhood has advan-tages as we have seen,it also has problems.A neighborhood centered on a corner or thin structure is dominated by the surround and computing the median results in oversmooth-ing as illustrated in Figure 3(a).Examining the non-local term suggests a solution.For a given pixel,if we know which other pixels in the area be-long to the same surface,we can weight them more highly.The modification to the objective function is achieved by introducing a weight into the non-local term [14,15]:∑i,j ∑(i ,j )∈N i,jw i,j,i ,j (|ˆu i,j −ˆu i ,j |+|ˆv i,j −ˆv i ,j |),(8)where w i,j,i ,j represents how likely pixel i ,j is to belongto the same surface as i,j .。

%双三次插值具体实现clc,clear;fff=imread('E:\Documents\BUPT\DIP\图片\lena.bmp');ff = rgb2gray(fff);%转化为灰度图像[mm,nn]=size(ff); %将图像隔行隔列抽取元素，得到缩小的图像fm=mm/2;n=nn/2;f = zeros(m,n);for i=1:mfor j=1:nf(i,j)=ff(2*i,2*j);endendk=5; %设置放大倍数bijiao1 = imresize(f,k,'bilinear');%双线性插值结果比较bijiao = uint8(bijiao1);a=f(1,:);c=f(m,:); %将待插值图像矩阵前后各扩展两行两列,共扩展四行四列b=[f(1,1),f(1,1),f(:,1)',f(m,1),f(m,1)];d=[f(1,n),f(1,n),f(:,n)',f(m,n),f(m,n)];a1=[a;a;f;c;c];b1=[b;b;a1';d;d];ffff=b1';f1=double(ffff);g1 = zeros(k*m,k*n);for i=1:k*m %利用双三次插值公式对新图象所有像素赋值u=rem(i,k)/k; i1=floor(i/k)+2;A=[sw(1+u) sw(u) sw(1-u) sw(2-u)];for j=1:k*nv=rem(j,k)/k;j1=floor(j/k)+2;C=[sw(1+v);sw(v);sw(1-v);sw(2-v)];B=[f1(i1-1,j1-1) f1(i1-1,j1) f1(i1-1,j1+1) f1(i1-1,j1+2)f1(i1,j1-1) f1(i1,j1) f1(i1,j1+1) f1(i1,j1+2)f1(i1+1,j1-1) f1(i1+1,j1) f1(i1+1,j1+1) f1(i1+1,j1+2)f1(i1+2,j1-1) f1(i1+2,j1) f1(i1+2,j1+1) f1(i1+2,j1+2)];g1(i,j)=(A*B*C);endendg=uint8(g1);imshow(uint8(f)); title('缩小的图像'); %显示缩小的图像figure,imshow(ff);title('原图'); %显示原图像figure,imshow(g);title('双三次插值放大的图像'); %显示插值后的图像figure,imshow(bijiao);title('双线性插值放大结果'); %显示插值后的图像mse=0;ff=double(ff);g=double(g);ff2=fftshift(fft2(ff)); %计算原图像和插值图像的傅立叶幅度谱g2=fftshift(fft2(g));figure,subplot(1,2,1),imshow(log(abs(ff2)),[8,10]);title('原图像的傅立叶幅度谱'); subplot(1,2,2),imshow(log(abs(g2)),[8,10]);title('双三次插值图像的傅立叶幅度谱');基函数代码：function A=sw(w1)w=abs(w1);if w<1&&w>=0A=1-2*w^2+w^3;elseif w>=1&&w<2A=4-8*w+5*w^2-w^3;elseA=0;end算法原理双三次插值又称立方卷积插值。

Package‘akima’September19,2011Version0.5-4Date2009-06-10Title Interpolation of irregularly spaced dataAuthor Fortran code by H.Akima R port by Albrecht Gebhardt<albrecht.gebhardt@uni-klu.ac.at>aspline function by ThomasPetzoldt<petzoldt@rcs.urz.tu-dresden.de>enhancements andcorrections by Martin Maechler<maechler@stat.math.ethz.ch>Maintainer Albrecht Gebhardt<albrecht.gebhardt@uni-klu.ac.at>Description Linear or cubic spline interpolation for irregular gridded dataLicensefile LICENSERepository CRANDate/Publication2009-11-0413:09:46R topics documented:akima (2)aspline (3)interp (5)interpp (8)Index1112akima akima Waveform Distortion Data for Bivariate InterpolationDescriptionakima is a list with components x,y and z which represents a smooth surface of z values at selected points irregularly distributed in the x-y plane.The data was taken from a study of waveform distortion in electronic circuits,described in:Hi-roshi Akima,"A Method of Bivariate Interpolation and Smooth Surface Fitting Based on Local Procedures",CACM,V ol.17,No.1,January1974,pp.18-20.ReferencesHiroshi Akima,"A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points",ACM Transactions on Mathematical Software,V ol.4,No.2,June1978, pp.148-159.Copyright1978,Association for Computing Machinery,Inc.,reprinted by permission. Examples##Not run:library(rgl)data(akima)#datargl.spheres(akima$x,akima$z,akima$y, .5,color="red")rgl.bbox()#bivariate linear interpolation#interp:akima.li<-interp(akima$x,akima$y,akima$z,xo=seq(min(akima$x),max(akima$x),length=1 ),yo=seq(min(akima$y),max(akima$y),length=1 ))#interp surface:rgl.surface(akima.li$x,akima.li$y,akima.li$z,color="green",alpha=c( .5))#interpp:akima.p<-interpp(akima$x,akima$y,akima$z,runif(2 ,min(akima$x),max(akima$x)),runif(2 ,min(akima$y),max(akima$y)))#interpp points:rgl.points(akima.p$x,akima.p$z,akima.p$y,size=4,color="yellow")#bivariate spline interpolation#datargl.spheres(akima$x,akima$z,akima$y, .5,color="red")rgl.bbox()#bivariate cubic spline interpolation#interp:akima.si<-interp(akima$x,akima$y,akima$z,xo=seq(min(akima$x),max(akima$x),length=1 ),yo=seq(min(akima$y),max(akima$y),length=1 ),linear=FALSE,extrap=TRUE)#interp surface:rgl.surface(akima.si$x,akima.si$y,akima.si$z,color="green",alpha=c( .5))#interpp:akima.sp<-interpp(akima$x,akima$y,akima$z,runif(2 ,min(akima$x),max(akima$x)),runif(2 ,min(akima$y),max(akima$y)),linear=FALSE,extrap=TRUE)#interpp points:rgl.points(akima.sp$x,akima.sp$z,akima.sp$y,size=4,color="yellow")##End(Not run)aspline Univariate Akima interpolationDescriptionThe function returns a list of points which smoothly interpolate given data points,similar to a curve drawn by hand.Usageaspline(x,y=NULL,xout,n=5 ,ties=mean,method="original",degree=3)Argumentsx,y vectors giving the coordinates of the points to be interpolated.Alternatively a single plotting structure can be specified:see xy.coords.xout an optional set of values specifying where interpolation is to take place.n If xout is not specified,interpolation takes place at n equally spaced points spanning the interval[min(x),max(x)].ties Handling of tied x values.Either a function with a single vector argument re-turning a single number result or the string"ordered".method either"original"method after Akima(1970)or"improved"method after Akima(1991)degree if improved algorithm is selected:degree of the polynomials for the interpolat-ing functionDetailsThe original algorithm is based on a piecewise function composed of a set of polynomials,each of degree three,at most,and applicable to successive interval of the given points.In this method, the slope of the curve is determined at each given point locally,and each polynomial representinga portion of the curve between a pair of given points is determined by the coordinates of and theslopes at the points.ValueA list with components x and y,containing n coordinates which interpolate the given data points. ReferencesAkima,H.(1970)A new method of interpolation and smooth curvefitting based on local proce-dures,J.ACM17(4),589-602Akima,H.(1991)A Method of Univariate Interpolation that Has the Accuracy of a Third-degree Polynomial.ACM Transactions on Mathematical Software,17(3),341-366.See Alsoapprox,splineExamples##regular spaced datax<-1:1y<-c(rnorm(5),c(1,1,1,1,3))xnew<-seq(-1,11, .1)plot(x,y,ylim=c(-3,3),xlim=range(xnew))lines(spline(x,y,xmin=min(xnew),xmax=max(xnew),n=2 ),col="blue")lines(aspline(x,y,xnew),col="red")lines(aspline(x,y,xnew,method="improved"),col="black",lty="dotted")lines(aspline(x,y,xnew,method="improved",degree=1 ),col="green",lty="dashed") ##irregular spaced datax<-sort(runif(1 ,max=1 ))y<-c(rnorm(5),c(1,1,1,1,3))xnew<-seq(-1,11, .1)plot(x,y,ylim=c(-3,3),xlim=range(xnew))lines(spline(x,y,xmin=min(xnew),xmax=max(xnew),n=2 ),col="blue")lines(aspline(x,y,xnew),col="red")lines(aspline(x,y,xnew,method="improved"),col="black",lty="dotted")lines(aspline(x,y,xnew,method="improved",degree=1 ),col="green",lty="dashed") ##an example of Akima,1991x<-c(-3,-2,-1, ,1,2,2.5,3)y<-c( , , , ,-1,-1, ,2)plot(x,y,ylim=c(-3,3))lines(spline(x,y,n=2 ),col="blue")lines(aspline(x,y,n=2 ),col="red")lines(aspline(x,y,n=2 ,method="improved"),col="black",lty="dotted")lines(aspline(x,y,n=2 ,method="improved",degree=1 ),col="green",lty="dashed")interp Gridded Bivariate Interpolation for Irregular DataDescriptionThese functions implement bivariate interpolation onto a grid for irregularly spaced input data.Bilinear or bicubic spline interpolation is applied using different versions of algorithms from Akima.Usageinterp(x,y,z,xo=seq(min(x),max(x),length=4 ),yo=seq(min(y),max(y),length=4 ),linear=TRUE,extrap=FALSE,duplicate="error",dupfun=NULL,ncp=NULL) interp.old(x,y,z,xo=seq(min(x),max(x),length=4 ),yo=seq(min(y),max(y),length=4 ),ncp= ,extrap=FALSE,duplicate="error",dupfun=NULL)interp.new(x,y,z,xo=seq(min(x),max(x),length=4 ),yo=seq(min(y),max(y),length=4 ),linear=FALSE,ncp=NULL,extrap=FALSE,duplicate="error",dupfun=NULL)Argumentsx vector of x-coordinates of data points.Missing values are not accepted.y vector of y-coordinates of data points.Missing values are not accepted.z vector of z-coordinates of data points.Missing values are not accepted.x,y,and z must be the same length and may contain no fewer than four points.The points of x and y cannot be collinear,i.e,they cannot fall on the same line(two vectors x and y such that y=ax+b for some a,b will not be accepted).interp is meant for cases in which you have x,y values scattered over a planeand a z value for each.If,instead,you are trying to evaluate a mathematicalfunction,or get a graphical interpretation of relationships that can be describedby a polynomial,try outer().xo vector of x-coordinates of output grid.The default is40points evenly spaced over the range of x.If extrapolation is not being used(extrap=FALSE,the de-fault),xo should have a range that is close to or inside of the range of x for theresults to be meaningful.yo vector of y-coordinates of output grid;analogous to xo,see above.linear logical–indicating wether linear or spline interpolation should be used.super-sedes old ncp parameterncp deprecated,use parameter linear.Now only used by interp.old().meaning was:number of additional points to be used in computing partialderivatives at each data point.ncp must be either (partial derivatives are notused),or at least2but smaller than the number of data points(and smaller than25).extrap logicalflag:should extrapolation be used outside of the convex hull determined by the data points?duplicate character string indicating how to handle duplicate data points.Possible values are"error"produces an error message,"strip"remove duplicate z values,"mean","median","user"calculate mean,median or user defined function(dupfun)of duplicate z values.dupfun a function,applied to duplicate points if duplicate="user".DetailsIf linear is TRUE(default),linear interpolation is used in the triangles bounded by data points.Cubic interpolation is done if linear is set to FALSE.If extrap is FALSE,z-values for points outside the convex hull are returned as NA.No extrapolation can be performed for the linear case.The interp function handles duplicate(x,y)points in different ways.As default it will stop with an error message.But it can give duplicate points an unique z value according to the parameter duplicate(mean,median or any other user defined function).The triangulation scheme used by interp works well if x and y have similar scales but will appear stretched if they have very different scales.The spreads of x and y must be within four orders of magnitude of each other for interp to work.Valuelist with3components:x,y vectors of x-and y-coordinates of output grid,the same as the input argument xo,or yo,if present.Otherwise,their default,a vector40points evenly spacedover the range of the input x.z matrix offitted z-values.The value z[i,j]is computed at the x,y point xo[i], yo[j].z has dimensions length(xo)times length(yo).Noteinterp is a wrapper for the two versions interp.old(it uses(almost)the same Fortran code from Akima1978as the S-Plus version)and interp.new(it is based on new Fortran code from Akima 1996).For linear interpolation the old version is choosen,but spline interpolation is done by the new version.Earlier versions(pre0.5-1)of interp used the parameter ncp to choose between linear and cubic interpolation,this is now done by setting the logical parameter e of ncp is still possible, but is deprecated.The resulting structure is suitable for input to the functions contour and image.Check the require-ments of these functions when choosing values for xo and yo.ReferencesAkima,H.(1978).A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points.ACM Transactions on Mathematical Software4,148-164.Akima,H.(1996).Algorithm761:scattered-data surfacefitting that has the accuracy of a cubic polynomial.ACM Transactions on Mathematical Software22,362–371.See Alsocontour,image,approx,spline,aspline,outer,expand.grid.Examplesdata(akima)plot(y~x,data=akima,main="akima example data")with(akima,text(x,y,formatC(z,dig=2),adj=- .1))##linear interpolationakima.li<-interp(akima$x,akima$y,akima$z)image(akima.li,add=TRUE)contour(akima.li,add=TRUE)points(akima,pch=3)##increase smoothness(using finer grid):akima.smooth<-with(akima,interp(x,y,z,xo=seq( ,25,length=1 ),yo=seq( ,2 ,length=1 )))image(akima.smooth,main="interp(<akima data>,*)on finer grid")contour(akima.smooth,add=TRUE,col="thistle")points(akima,pch=3,cex=2,col="blue")#use triangulation package to show underlying triangulation:if(library(tripack,logical.return=TRUE))plot(tri.mesh(akima),add=TRUE,lty="dashed")#use only15points(interpolation only within convex hull!)akima.part<-with(akima,interp(x[1:15],y[1:15],z[1:15]))image(akima.part)title("interp()on subset of only15points")contour(akima.part,add=TRUE)points(akima$x[1:15],akima$y[1:15],col="blue")##spline interpolation,two variants(AMS526"Old",AMS761"New")##-----------------------------------------------------------------##"Old":use5points to calculate derivatives->many NAsakima.sO<-interp.old(akima$x,akima$y,akima$z,xo=seq( ,25,length=1 ),yo=seq( ,2 ,length=1 ),ncp=5) table(is.na(akima.sO$z))##399 NA’s;=4 %akima.sO<-with(akima,interp.old(x,y,z,xo=seq( ,25,length=1 ),yo=seq( ,2 ,len=1 ),ncp=4)) sum(is.na(akima.sO$z))##still3429image(akima.sO,main="interp.old(*,ncp=4)[almost useless]")contour(akima.sO,add=TRUE)##"New:"akima.spl<-with(akima,interp.new(x,y,z,xo=seq( ,25,length=1 ),yo=seq( ,2 ,length=1 ))) ##equivalent call via setting linear=FALSE in interp():akima.spl<-with(akima,interp(x,y,z,xo=seq( ,25,length=1 ),yo=seq( ,2 ,length=1 ),linear=FALSE))contour(akima.spl,main="smooth interp(*,linear=FALSE)")points(akima)full.pal<-function(n)hcl(h=seq(34 ,2 ,length=n))cool.pal<-function(n)hcl(h=seq(12 , ,length=n)+15 )warm.pal<-function(n)hcl(h=seq(12 , ,length=n)-3 )filled.contour(akima.spl,color.palette=full.pal,plot.axes={axis(1);axis(2);title("smooth interp(*,linear=FALSE)");points(akima,pch=3,col=hcl(c=1 ,l=2 ))}) #no extrapolation!##example with duplicate points:data(airquality)air<-subset(airquality,!is.na(Temp)&!is.na(Ozone)&!is.na(Solar.R))#gives an error{duplicate..}:try(air.ip<-interp(air$Temp,air$Solar.R,air$Ozone,linear=FALSE))#use mean of duplicate points:air.ip<-with(air,interp(Temp,Solar.R,log(Ozone),duplicate="mean",linear=FALSE))image(air.ip,main="Airquality:Ozone vs.Temp and Solar.R")with(air,points(Temp,Solar.R))interpp Pointwise Bivariate Interpolation for Irregular DataDescriptionIf ncp is zero,linear interpolation is used in the triangles bounded by data points.Cubic interpo-lation is done if partial derivatives are used.If extrap is FALSE,z-values for points outside the convex hull are returned as NA.No extrapolation can be performed if ncp is zero.The interpp function handles duplicate(x,y)points in different ways.As default it will stop with an error message.But it can give duplicate points an unique z value according to the parameter duplicate(mean,median or any other user defined function).The triangulation scheme used by interp works well if x and y have similar scales but will appear stretched if they have very different scales.The spreads of x and y must be within four orders of magnitude of each other for interpp to work.Usageinterpp(x,y,z,xo,yo,linear=TRUE,extrap=FALSE,duplicate="error",dupfun=NULL,ncp)Argumentsx vector of x-coordinates of data points.Missing values are not accepted.y vector of y-coordinates of data points.Missing values are not accepted.z vector of z-coordinates of data points.Missing values are not accepted.x,y,and z must be the same length and may contain no fewer than four points.The points of x and y cannot be collinear,i.e,they cannot fall on the same line(two vectors x and y such that y=ax+b for some a,b will not be accepted).xo vector of x-coordinates of points at which to evaluate the interpolating function.yo vector of y-coordinates of points at which to evaluate the interpolating function.linear logical–indicating wether linear or spline interpolation should be used.super-sedes old ncp parameterncp deprecated,use parameter linear.Now only used by interpp.old().meaning was:number of additional points to be used in computing partialderivatives at each data point.ncp must be either (partial derivatives are notused,=linear interpolation),or at least2but smaller than the number of datapoints(and smaller than25).extrap logicalflag:should extrapolation be used outside of the convex hull determinedby the data points?duplicate indicates how to handle duplicate data points.Possible values are"error"-pro-duces an error message,"strip"-remove duplicate z values,"mean","median","user"-calculate mean,median or user defined function of duplicate z values.dupfun this function is applied to duplicate points if duplicate="user"Valuelist with3components:x vector of x-coordinates of output points,the same as the input argument xo.y vector of y-coordinates of output points,the same as the input argument yo.zfitted z-values.The value z[i]is computed at the x,y point x[i],y[i].NOTEUse interp if interpolation on a regular grid is wanted.The two versions interpp.old and interpp.new refer to Akimas Fortran code from1978and1996resp.The call wrapper interpp chooses interpp.old for linear and interpp.new for cubicspline interpolation.Earlier versions(pre0.5-1)of interpp used the parameter ncp to choose between linear and cubicinterpolation,this is now done by setting the logical parameter e of ncp is still possible,but is deprecated.ReferencesAkima,H.(1978).A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points.ACM Transactions on Mathematical Software,4,148-164.Akima,H.(1996).Algorithm761:scattered-data surfacefitting that has the accuracy of a cubic polynomial.ACM Transactions on Mathematical Software,22,362-371.See Alsocontour,image,approxfun,splinefun,outer,expand.grid,interp,aspline.Examplesdata(akima)#linear interpolation at points(1,2),(5,6)and(1 ,12)akima.lip<-interpp(akima$x,akima$y,akima$z,c(1,5,1 ),c(2,6,12))akima.lip$z#spline interpolationakima.sip<-interpp(akima$x,akima$y,akima$z,c(1,5,1 ),c(2,6,12),linear=FALSE)akima.sip$zIndex∗Topic arithaspline,3∗Topic datasetsakima,2∗Topic dplotaspline,3interp,5interpp,8akima,2approx,4,7approxfun,10aspline,3,7,10contour,6,7,10expand.grid,7,10image,6,7,10interp,5,10interpp,8outer,7,10spline,4,7splinefun,10xy.coords,311。

1Image Super-Resolution via Sparse Representation Jianchao Yang,Student Member,IEEE,John Wright,Student Member,IEEE Thomas Huang,Life Fellow,IEEEand Yi Ma,Senior Member,IEEEAbstract—This paper presents a new approach to single-image superresolution,based on sparse signal representation.Research on image statistics suggests that image patches can be well-represented as a sparse linear combination of elements from an appropriately chosen over-complete dictionary.Inspired by this observation,we seek a sparse representation for each patch of the low-resolution input,and then use the coefficients of this representation to generate the high-resolution output.Theoretical results from compressed sensing suggest that under mild condi-tions,the sparse representation can be correctly recovered from the downsampled signals.By jointly training two dictionaries for the low-and high-resolution image patches,we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries.Therefore,the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch. The learned dictionary pair is a more compact representation of the patch pairs,compared to previous approaches,which simply sample a large amount of image patch pairs[1],reducing the computational cost substantially.The effectiveness of such a sparsity prior is demonstrated for both general image super-resolution and the special case of face hallucination.In both cases,our algorithm generates high-resolution images that are competitive or even superior in quality to images produced by other similar SR methods.In addition,the local sparse modeling of our approach is naturally robust to noise,and therefore the proposed algorithm can handle super-resolution with noisy inputs in a more unified framework.I.I NTRODUCTIONSuper-resolution(SR)image reconstruction is currently a very active area of research,as it offers the promise of overcoming some of the inherent resolution limitations of low-cost imaging sensors(e.g.cell phone or surveillance cameras)allowing better utilization of the growing capability of high-resolution displays(e.g.high-definition LCDs).Such resolution-enhancing technology may also prove to be essen-tial in medical imaging and satellite imaging where diagnosis or analysis from low-quality images can be extremely difficult. Conventional approaches to generating a super-resolution im-age normally require as input multiple low-resolution images of the same scene,which are aligned with sub-pixel accuracy. The SR task is cast as the inverse problem of recovering the original high-resolution image by fusing the low-resolution images,based on reasonable assumptions or prior knowledge about the observation model that maps the high-resolution im-age to the low-resolution ones.The fundamental reconstruction Jianchao Yang and Thomas Huang are with Beckman Institute,Uni-versity of Illinois Urbana-Champaign,Urbana,IL61801USA(email: jyang29@;huang@).John Wright and Yi Ma are with CSL,University of Illinois Urbana-Champaign,Urbana,IL61801USA(email:jnwright@; yima@).constraint for SR is that the recovered image,after applying the same generation model,should reproduce the observed low-resolution images.However,SR image reconstruction is gen-erally a severely ill-posed problem because of the insufficient number of low resolution images,ill-conditioned registration and unknown blurring operators,and the solution from the reconstruction constraint is not unique.Various regularization methods have been proposed to further stabilize the inversion of this ill-posed problem,such as[2],[3],[4].However,the performance of these reconstruction-based super-resolution algorithms degrades rapidly when the desired magnification factor is large or the number of available input images is small.In these cases,the result may be overly smooth,lacking important high-frequency details[5].Another class of SR approach is based on interpolation[6],[7], [8].While simple interpolation methods such as Bilinear or Bicubic interpolation tend to generate overly smooth images with ringing and jagged artifacts,interpolation by exploiting the natural image priors will generally produce more favorable results.Dai et al.[7]represented the local image patches using the background/foreground descriptors and reconstructed the sharp discontinuity between the two.Sun et.al.[8]explored the gradient profile prior for local image structures and ap-plied it to super-resolution.Such approaches are effective in preserving the edges in the zoomed image.However,they are limited in modeling the visual complexity of the real images. For natural images withfine textures or smooth shading,these approaches tend to produce watercolor-like artifacts.A third category of SR approach is based on ma-chine learning techniques,which attempt to capture the co-occurrence prior between low-resolution and high-resolution image patches.[9]proposed an example-based learning strat-egy that applies to generic images where the low-resolution to high-resolution prediction is learned via a Markov Random Field(MRF)solved by belief propagation.[10]extends this approach by using the Primal Sketch priors to enhance blurred edges,ridges and corners.Nevertheless,the above methods typically require enormous databases of millions of high-resolution and low-resolution patch pairs,and are therefore computationally intensive.[11]adopts the philosophy of Lo-cally Linear Embedding(LLE)[12]from manifold learning, assuming similarity between the two manifolds in the high-resolution and the low-resolution patch spaces.Their algorithm maps the local geometry of the low-resolution patch space to the high-resolution one,generating high-resolution patch as a linear combination of ing this strategy,more patch patterns can be represented using a smaller training database.However,using afixed number K neighbors for reconstruction often results in blurring effects,due to over-or under-fitting.In our previous work[1],we proposed a method2for adaptively choosing the most relevant reconstruction neigh-bors based on sparse coding,avoiding over-or under-fitting of [11]and producing superior results.However,sparse codingover a large sampled image patch database directly is too time-consuming.While the mentioned approaches above were proposed forgeneric image super-resolution,specific image priors can be incorporated when tailored to SR applications for specificdomains such as human faces.This face hallucination prob-lem was addressed in the pioneering work of Baker and Kanade[13].However,the gradient pyramid-based predictionintroduced in[13]does not directly model the face prior,and the pixels are predicted individually,causing discontinuities and artifacts.Liu et al.[14]proposed a two-step statisticalapproach integrating the global PCA model and a local patch model.Although the algorithm yields good results,the holistic PCA model tends to yield results like the mean face and theprobabilistic local patch model is complicated and compu-tationally demanding.Wei Liu et al.[15]proposed a newapproach based on TensorPatches and residue compensation. While this algorithm adds more details to the face,it also introduces more artifacts.This paper focuses on the problem of recovering the super-resolution version of a given low-resolution image.Similar to the aforementioned learning-based methods,we will relyon patches from the input image.However,instead of work-ing directly with the image patch pairs sampled from high-and low-resolution images[1],we learn a compact repre-sentation for these patch pairs to capture the co-occurrence prior,significantly improving the speed of the algorithm.Our approach is motivated by recent results in sparse signal representation,which suggest that the linear relationships among high-resolution signals can be accurately recoveredfrom their low-dimensional projections[16],[17].Although the super-resolution problem is very ill-posed,making preciserecovery impossible,the image patch sparse representation demonstrates both effectiveness and robustness in regularizing the inverse problem.a)Basic Ideas:To be more precise,let D∈R n×K be an overcomplete dictionary of K atoms(K>n),and suppose a signal x∈R n can be represented as a sparse linearcombination with respect to D.That is,the signal x can be written as x=Dα0where whereα0∈R K is a vector with very few( n)nonzero entries.In practice,we might onlyobserve a small set of measurements y of x:y.=L x=L Dα0,(1) where L∈R k×n with k<n is a projection matrix.In our super-resolution context,x is a high-resolution image(patch), while y is its low-resolution counter part(or features extracted from it).If the dictionary D is overcomplete,the equation x=Dαis underdetermined for the unknown coefficientsα. The equation y=L Dαis even more dramatically under-determined.Nevertheless,under mild conditions,the sparsest solutionα0to this equation will be unique.Furthermore,if D satisfies an appropriate near-isometry condition,then for a wide variety of matrices L,any sufficiently sparse linear representation of a high-resolution image patch x interms Fig.1.Reconstruction of a raccoon face with magnification factor2.Left: result by our method.Right:the original image.There is little noticeable difference visually even for such a complicated texture.The RMSE for the reconstructed image is5.92(only the local patch model is employed).of the D can be recovered(almost)perfectly from the low-resolution image patch[17],[18].1Fig.1shows an example that demonstrates the capabilities of our method derived fromthis principle.The image of the raccoon face is blurred anddownsampled to half of its original size in both dimensions. Then we zoom the low-resolution image to the original sizeusing the proposed method.Even for such a complicated texture,sparse representation recovers a visually appealingreconstruction of the original signal.Recently sparse representation has been successfully appliedto many other related inverse problems in image processing, such as denoising[19]and restoration[20],often improving onthe state-of-the-art.For example in[19],the authors use theK-SVD algorithm[21]to learn an overcomplete dictionary from natural image patches and successfully apply it to theimage denoising problem.In our setting,we do not directlycompute the sparse representation of the high-resolution patch. Instead,we will work with two coupled dictionaries,D h forhigh-resolution patches,and D l for low-resolution ones.The sparse representation of a low-resolution patch in terms of D l will be directly used to recover the corresponding high-resolution patch from D h.We obtain a locally consistent solution by allowing patches to overlap and demanding that thereconstructed high-resolution patches agree on the overlappedareas.In this paper,we try to learn the two overcomplete dictionaries in a probabilistic model similar to[22].To enforce that the image patch pairs have the same sparse representations with respect to D h and D l,we learn the two dictionaries simultaneously by concatenating them with proper normal-ization.The learned compact dictionaries will be applied to both generic image super-resolution and face hallucination to demonstrate their effectiveness.Compared with the aforementioned learning-based methods,our algorithm requires only two compact learned dictionaries, instead of a large training patch database.The computation, mainly based on linear programming or convex optimization, is much more efficient and scalable,compared with[9],[10], [11].The online recovery of the sparse representation uses the low-resolution dictionary only–the high-resolution dictionary 1Even though the structured projection matrix defined by blurring and downsampling in our SR context does not guarantee exact recovery ofα0, empirical experiments indeed demonstrate the effectiveness of such a sparse prior for our SR tasks.3is used to calculate thefinal high-resolution image.The computed sparse representation adaptively selects the most relevant patch bases in the dictionary to best represent each patch of the given low-resolution image.This leads to superior performance,both qualitatively and quantitatively,compared to the method described in[11],which uses afixed number of nearest neighbors,generating sharper edges and clearer textures.In addition,the sparse representation is robust to noise as suggested in[19],and thus our algorithm is more robust to noise in the test image,while most other methods cannot perform denoising and super-resolution simultaneously.b)Organization of the Paper:The remainder of this paper is organized as follows.Section II details our formula-tion and solution to the image super-resolution problem based on sparse representation.Specifically,we study how to apply sparse representation for both generic image super-resolution and face hallucination.In Section III,we discuss how to learn the two dictionaries for the high-and low-resolution image patches respectively.Various experimental results in Section IV demonstrate the efficacy of sparsity as a prior for regularizing image super-resolution.c)Notations:X and Y denote the high-and low-resolution images respectively,and x and y denote the high-and low-resolution image patches respectively.We use bold uppercase D to denote the dictionary for sparse coding, specifically we use D h and D l to denote the dictionaries for high-and low-resolution image patches respectively.Bold lowercase letters denote vectors.Plain uppercase letters denote regular matrices,i.e.,S is used as a downsampling operation in matrix form.Plain lowercase letters are used as scalars.II.I MAGE S UPER-R ESOLUTION FROM S PARSITYThe single-image super-resolution problem asks:given a low-resolution image Y,recover a higher-resolution image X of the same scene.Two constraints are modeled in this work to solve this ill-posed problem:1)reconstruction constraint, which requires that the recovered X should be consistent with the input Y with respect to the image observation model; and2)sparsity prior,which assumes that the high resolution patches can be sparsely represented in an appropriately chosen overcomplete dictionary,and that their sparse representations can be recovered from the low resolution observation.1)Reconstruction constraint:The observed low-resolution image Y is a blurred and downsampled version of the high resolution image X:Y=SH X(2) Here,H represents a blurringfilter,and S the downsampling operator.Super-resolution remains extremely ill-posed,since for a given low-resolution input Y,infinitely many high-resolution images X satisfy the above reconstruction constraint.We further regularize the problem via the following prior on small patches x of X:2)Sparsity prior:The patches x of the high-resolution image X can be represented as a sparse linear combination in a dictionary D h trained from high-resolution patches sampled from training images:x≈D hαfor someα∈R K with α 0 K.(3) The sparse representationαwill be recovered by representing patches y of the input image Y,with respect to a low resolution dictionary D l co-trained with D h.The dictionary training process will be discussed in Section III.We apply our approach to both generic images and face images.For generic image super-resolution,we divide the problem into two steps.First,as suggested by the sparsity prior(3),wefind the sparse representation for each local patch,respecting spatial compatibility between neighbors. Next,using the result from this local sparse representation, we further regularize and refine the entire image using the reconstruction constraint(2).In this strategy,a local model from the sparsity prior is used to recover lost high-frequency for local details.The global model from the reconstruction constraint is then applied to remove possible artifacts from thefirst step and make the image more consistent and natural. The face images differ from the generic images in that the face images have more regular structure and thus reconstruction constraints in the face subspace can be more effective.For face image super-resolution,we reverse the above two steps to make better use of the global face structure as a regularizer. Wefirstfind a suitable subspace for human faces,and apply the reconstruction constraints to recover a medium resolution image.We then recover the local details using the sparsity prior for image patches.The remainder of this section is organized as follows:in Section II-A,we discuss super-resolution for generic images. We will introduce the local model based on sparse represen-tation and global model based on reconstruction constraints. In Section II-B we discuss how to introduce the global face structure into this framework to achieve more accurate and visually appealing super-resolution for face images.A.Generic Image Super-Resolution from Sparsity1)Local model from sparse representation:Similar to the patch-based methods mentioned previously,our algorithm tries to infer the high-resolution image patch for each low-resolution image patch from the input.For this local model, we have two dictionaries D h and D l,which are trained to have the same sparse representations for each high-resolution and low-resolution image patch pair.We subtract the mean pixel value for each patch,so that the dictionary represents image textures rather than absolute intensities.In the recovery process,the mean value for each high-resolution image patch is then predicted by its low-resolution version.For each input low-resolution patch y,wefind a sparse representation with respect to D l.The corresponding high-resolution patch bases D h will be combined according to these coefficients to generate the output high-resolution patch x. The problem offinding the sparsest representation of y can be formulated as:min α 0s.t. F D lα−F y 22≤ ,(4)4 where F is a(linear)feature extraction operator.The main roleof F in(4)is to provide a perceptually meaningful constraint2on how closely the coefficientsαmust approximate y.We willdiscuss the choice of F in Section III.Although the optimization problem(4)is NP-hard in gen-eral,recent results[23],[24]suggest that as long as the desiredcoefficientsαare sufficiently sparse,they can be efficientlyrecovered by instead minimizing the 1-norm3,as follows:min α 1s.t. F D lα−F y 22≤ .(5)Lagrange multipliers offer an equivalent formulationminαF D lα−F y 22+λ α 1,(6)where the parameterλbalances sparsity of the solutionandfidelity of the approximation to y.Notice that this isessentially a linear regression regularized with 1-norm on thecoefficients,known in statistical literature as the Lasso[27].Solving(6)individually for each local patch does notguarantee the compatibility between adjacent patches.Weenforce compatibility between adjacent patches using a one-pass algorithm similar to that of[28].4The patches areprocessed in raster-scan order in the image,from left to rightand top to bottom.We modify(5)so that the super-resolutionreconstruction D hαof patch y is constrained to closelyagree with the previously computed adjacent high-resolutionpatches.The resulting optimization problem ismin α 1s.t. F D lα−F y 22≤ 1,P D hα−w 22≤ 2,(7)where the matrix P extracts the region of overlap betweenthe current target patch and previously reconstructed high-resolution image,and w contains the values of the previouslyreconstructed high-resolution image on the overlap.The con-strained optimization(7)can be similarly reformulated as:minα˜Dα−˜y 22+λ α 1,(8)where˜D=F D lβP D hand˜y=F yβw.The parameterβcontrols the tradeoff between matching the low-resolution input andfinding a high-resolution patch that is compatible with its neighbors.In all our experiments,we simply set β=1.Given the optimal solutionα∗to(8),the high-resolution patch can be reconstructed as x=D hα∗.2Traditionally,one would seek the sparsestαs.t. D lα−y 2≤ .For super-resolution,it is more appropriate to replace this2-norm with a quadratic norm · F T F that penalizes visually salient high-frequency errors.3There are also some recent works showing certain non-convex optimization problems can produce superior sparse solutions to the 1convex problem,e.g., [25]and[26].4There are different ways to enforce compatibility.In[11],the values in the overlapped regions are simply averaged,which will result in blurring effects. The greedy one-pass algorithm[28]is shown to work almost as well as the use of a full MRF model[9].Our algorithm,not based on the MRF model, is essentially the same by trusting partially the previously recovered high resolution image patches in the overlapped regions.Algorithm1(Super-Resolution via Sparse Representation). 1:Input:training dictionaries D h and D l,a low-resolutionimage Y.2:For each3×3patch y of Y,taken starting from the upper-left corner with1pixel overlap in each direction,•Compute the mean pixel value m of patch y.•Solve the optimization problem with˜D and˜y definedin(8):minα ˜Dα−˜y 22+λ α 1.•Generate the high-resolution patch x=D hα∗.Putthe patch x+m into a high-resolution image X0. 3:End4:Using gradient descent,find the closest image to X0 which satisfies the reconstruction constraint:X∗=arg minXSH X−Y 22+c X−X0 22.5:Output:super-resolution image X∗.2)Enforcing global reconstruction constraint:Notice that (5)and(7)do not demand exact equality between the low-resolution patch y and its reconstruction D lα.Because of this,and also because of noise,the high-resolution image X0produced by the sparse representation approach of the previous section may not satisfy the reconstruction constraint (2)exactly.We eliminate this discrepancy by projecting X0 onto the solution space of SH X=Y,computingX∗=arg minXSH X−Y 22+c X−X0 22.(9) The solution to this optimization problem can be efficiently computed using gradient descent.The update equation for this iterative method isX t+1=X t+ν[H T S T(Y−SH X t)+c(X−X0)],(10) where X t is the estimate of the high-resolution image after the t-th iteration,νis the step size of the gradient descent. We take result X∗from the above optimization as our final estimate of the high-resolution image.This image is as close as possible to the initial super-resolution X0given by sparsity,while respecting the reconstruction constraint.The entire super-resolution process is summarized as Algorithm1.3)Global optimization interpretation:The simple SR algo-rithm outlined in the previous two subsections can be viewed as a special case of a more general sparse representation framework for inverse problems in image processing.Related ideas have been profitably applied in image compression, denoising[19],and restoration[20].In addition to placing our work in a larger context,these connections suggest means of further improving the performance,at the cost of increased computational complexity.Given sufficient computational resources,one could in prin-ciple solve for the coefficients associated with all patches simultaneously.Moreover,the entire high-resolution image X itself can be treated as a variable.Rather than demanding that X be perfectly reproduced by the sparse coefficientsα,we can penalize the difference between X and the high-resolution image given by these coefficients,allowing solutions that5are not perfectly sparse,but better satisfy the reconstruction constraints.This leads to a large optimization problem:X ∗=arg min X ,{αij }SH X −Y 22+λi,jαij 0+γi,jD h αij −P ij X 22+τρ(X ) .(11)Here,αij denotes the representation coefficients for the (i,j )th patch of X ,and P ij is a projection matrix that selects the (i,j )th patch from X .ρ(X )is a penalty function that encodes additional prior knowledge about the high-resolution image.This function may depend on the image category,or may take the form of a generic regularization term (e.g.,Huber MRF,Total Variation,Bilateral Total Variation).Algorithm 1can be interpreted as a computationally efficient approximation to (11).The sparse representation step recovers the coefficients αby approximately minimizing the sum of the second and third terms of (11).The sparsity term αij 0is relaxed to αij 1,while the high-resolution fidelity term D h αij −P ij X 2is approximated by its low-resolution version F D l αij −F y ij 2.Notice,that if the sparse coefficients αare fixed,the third term of (11)essentially penalizes the difference between the super-resolution image X and the reconstruction given by the coefficients: i,j D h αij −P ij X 22≈ X 0−X 22.Hence,for small γ,the back-projection step of Algorithm 1approximately minimizes the sum of the first and third terms of (11).Algorithm 1does not,however,incorporate any prior be-sides sparsity of the representation coefficients –the term ρ(X )is absent in our approximation.In Section IV we will see that sparsity in a relevant dictionary is a strong enough prior that we can already achieve good super-resolution per-formance.Nevertheless,in settings where further assumptions on the high-resolution signal are available,these priors can be incorperated into the global reconstruction step of our algorithm.B.Face super-resolution from SparsityFace image resolution enhancement is usually desirable in many surveillance scenarios,where there is always a large distance between the camera and the objects (people)of interest.Unlike the generic image super-resolution discussed earlier,face images are more regular in structure and thus should be easier to handle.Indeed,for face super-resolution,we can deal with lower resolution input images.The basic idea is first to use the face prior to zoom the input to a reasonable medium resolution,and then to employ the local sparsity prior model to recover details.To be precise,the solution is also approached in two steps:1)global model:use reconstruction constraint to recover a medium high-resolution face image,but the solution is searched only in the face subspace;and 2)local model:use the local sparse model to recover the image details.a)Non-negative matrix factorization:In face super-resolution,the most frequently used subspace method for mod-eling the human face is Principal Component Analysis (PCA),which chooses a low-dimensional subspace that captures as much of the variance as possible.However,the PCA bases are holistic,and tend to generate smooth faces similar to the mean.Moreover,because principal component representations allow negative coefficients,the PCA reconstruction is often hard to interpret.Even though faces are objects with lots of variance,they are made up of several relatively independent parts such as eyes,eyebrows,noses,mouths,checks and chins.Nonnegative Matrix Factorization (NMF)[29]seeks a representation of the given signals as an additive combination of local features.To find such a part-based subspace,NMF is formulated as the following optimization problem:arg min U,VX −UV 22s.t.U ≥0,V ≥0,(12)where X ∈R n ×m is the data matrix,U ∈R n ×r is the basismatrix and V ∈R r ×m is the coefficient matrix.In our context here,X simply consists of a set of pre-aligned high-resolution training face images as its column vectors.The number of the bases r can be chosen as n ∗m/(n +m )which is smaller than n and m ,meaning a more compact representation.It can be shown that a locally optimum of (12)can be obtained via the following update rules:V ij ←−V ij (U T X )ij(U TUV )ij U ki ←−U ki (XV T )ki(UV V T )ki,(13)where 1≤i ≤r ,1≤j ≤m and 1≤k ≤n .The obtained basis matrix U is often sparse and localized.b)Two step face super-resolution:Let X and Y denote the high resolution and low resolution faces respectively.Y is obtained from X by smoothing and downsampling as in Eq.2.We want to recover X from the observation Y .In this paper,we assume Y has been pre-aligned to the training database by either manually labeling the feature points or with some automatic face alignment algorithm such as the method used in [14].We can achieve the optimal solution for X based on the Maximum a Posteriori (MAP)criteria,X ∗=arg max Xp (Y |X )p (X ).(14)p (Y |X )models the image observation process,usually with Gaussian noise assumption on the observation Y ,p (Y |X )=1/Z exp(− SHU c −Y 22/(2∗σ2))with Z being a nor-malization factor.p (X )is a prior on the underlying high resolution image X ,typically in the exponential form p (X )=exp(−cρ(X )).Using the rules in (13),we can obtain the basis matrix U ,which is composed of sparse bases.Let Ωdenote the face subspace spanned by U .Then in the subspace Ω,the super-resolution problem in (14)can be formulated using the reconstruction constraints as:c ∗=arg min cSHU c −Y 22+ηρ(U c )s.t.c ≥0,(15)where ρ(U c )is a prior term regularizing the high resolution solution,c ∈R r ×1is the coefficient vector in the subspace Ω。

抑制TLR4对急性呼吸窘迫综合征小鼠的保护作用及机制研究姜芸郭红摘要目的探究抑制TLR4对脂多糖诱导的小鼠急性呼吸窘迫综合征的保护作用及机制。

方法45只BALB/c小鼠随机分为对照组.ARDS组及TLR4抑制剂TAK242组,ARDS小鼠模型采用脂多糖(LPS)构建，试验组用TAK242进行干预。

各组小鼠行血气分析；ELISA检测血清炎性因子TNF-a、IL-6水平；HE染色检测各组小鼠肺组织病理变化；免疫组化检测肺组织TNF-a、IL-6表达水平；Western blot法检测肺组织TLR4、NF-k B蛋白表达。

结果与对照组比较，ARDS组小鼠PaO2/FiO2值显著降低(P<0.05),血清炎性因子TNF-a、IL-6水平显著增加(P<0.05),TLR4、NF-k B表达水平均显著升高(P< 0.05)。

与ARDS组比较,TAK242组小鼠PaO2/FiO2值显著增加(P<0.05),血清炎性因子TNF-a、IL-6水平显著降低(P<0.05)o TLR4、NF-k B表达水平均显著降低(P<0.05)o病理切片结果显示,ARDS组小鼠肺组织结构损伤严重，TNF-a、IL-6表达增加(P<0.05)；TAK242组小鼠肺组织损伤显著缓解(P<0.05),TNF-a、IL-6表达降低(P<0.05)。

结论抑制TLR4可以抑制下游NF-k B信号通路进而减轻LPS诱导的小鼠肺组织的炎性反应。

关键词TLR4急性呼吸窘迫综合征炎性反应中图分类号R5文献标识码A DOI10.11969/j .issn.1673-548X.2021.01.017Study on the Protective Effects and Mechanism of Inhibiting Toll-like Receptor4on ARDS in Mice.Jiang Yun,Guo Hong.Oncocardiol-ogy Department,Xin/iang Medical University Affiliated Tumor Hospital,Xinjiang830011,ChinaAbstract Objective To explore the protective effects and mechanism of inhibiting Toll-like receptor4(TLR4)on acute respira-Lory distress syndrome(ARDS)in mice.Methods Forty five BALB/c mice were randomly divided into control group,ARDS group and TLR4inhibitor TAK242group.Lipopolysaccharide was used to induce ARDS model in mice and TAK242was intervened in the TAK242 group.Blood gas analysis were performed on mice；ELISA was used to detect serum TNF-a and IL-6levels.HE staining was used to detect the pathological changes in lung tissue of mice in each group.Immunohistochemistry was used to detect lung TNF一a and IL-6ex­pression levels.The expression of TLR4and NF一k B proteins in lung tissue were detected by Western blot.Results Compared with the control group,the PaO2/FiO2value in the ARDS group was significantly reduced(P<0.05),the contents of serum TNF一a and IL-6 were significantly increased(P<0.05),and the expression levels of TLR4and NF一k B were significantly increased(P<0.05).When compared with mice in the ARDS group,PaO2/FiO2value in the TAK242group significantly was increased(P<0.05),and the contents of serum TNF一a and IL-6were significantly decreased(P<0.05),while the expression levels of TLR4and NF一k B were significantly reduced(P<0.05).HE staining showed that the lung tissue was severely damaged in ARDS group and the expression of TNF-a and IL-6was increased(P<0.05).The lung tissue in TAK242group was significantly alleviated and the expressions of TNF-a and IL-6were decreased when compared with the ARDS group(P<0.05).Conclusion TAK242alleviate ARDS by blocking TLR4and inhibi­ting the downstream NF一k B signaling pathway,which suppresses the inflammatory response in mice.Key words TLR4；Acute respiratory distress syndrome；Inflammatory reaction急性呼吸窘迫综合征(acute respiratory distress syndrome,ARDS)是一种危及生命的呼吸系统疾病,是危重症医学中最具有挑战性的临床疾病之一。

改进相似性度量模型的单幅图像自学习超分辨算法赵丽玲;孙权森【摘要】在自学习超分辨算法中,高低分辨率图像块匹配是否准确是算法的关键.在高低分辨率图像块匹配过程中,考虑图像块纹理结构的重要性,提出了一种基于纹理约束的图像块相似性度量模型,应用该模型完成了高低分辨率图像块更为准确的匹配,使超分辨结果图像的细节更加丰富,进一步提高了图像质量.该算法仅使用了单幅低分辨率图像自身的相关先验信息,有效提升了图像的空间分辨率.实验结果表明,与双三次插值算法、自相似学习超分辨算法相比,本文提出的算法超分辨视觉效果更好,并且在客观评价指标中同样表现良好.%The accurate matching of high and low resolution image blocks is the key of self-examples super resolution algorithm.In the process of blocks matching of high and low resolution images,considering the importance of texture image block structure,a similarity metric model based on constrained texture image patch is proposed in this paper.By using this exact matching model,the detail of super-resolution result image is further enriched,and the image quality is improved also.The new algorithm has the particular advantage of improving spatial resolution of image only using prior information of single low-resolution image itself.The experimental results show that the proposed algorithm has a better super-resolution visual effect compared with the bicubic interpolation algorithm and the local self-examples super-resolution algorithm,and it also has a good performance in the objective evaluation index.【期刊名称】《数据采集与处理》【年(卷),期】2018(033)002【总页数】8页(P240-247)【关键词】相似性度量;方差;自学习;单幅图像;超分辨率【作者】赵丽玲;孙权森【作者单位】南京理工大学计算机科学与工程学院,南京,210094;南京信息工程大学信息与控制学院,南京,210044;南京理工大学计算机科学与工程学院,南京,210094【正文语种】中文【中图分类】TP391.4引言高分辨率数字图像在遥感图像分析、医学检测、交通监控及公共安全等领域具有重要应用研究价值，有利于对感兴趣目标的提取、分析、检测和识别等。

Chapter8Curve and Surface Fitting1Scope of the ChapterThis chapter is concerned with the interpolation and approximation of data sets in one,two or three dimensions.The approximating functions available are Chebyshev polynomials,piecewise cubic Hermite polynomials,cubic splines,bicubic splines,and interpolants produced by a modification of Shepard’s method(see Renka[2]).2Available ModulesModule8.1:nag pch interp—Piecewise cubic Hermite interpolationProvides procedures for computing and evaluating piecewise cubic Hermite interpolants to arbitrary data sets in one dimension.In particular,the module contains procedures for:•generating a monotonicity-preserving interpolant;•evaluating a piecewise cubic Hermite polynomial;•integrating a piecewise cubic Hermite polynomial.Module8.2:nag spline1d—One-dimensional splinefittingProvides procedures for computing and evaluating spline approximations to arbitrary data sets in one dimension.Procedures are available for:•generating a cubic spline interpolant;•generating a least-squares cubic splinefit with given interior knots;•generating a cubic spline approximation with automatic knot placement;•computing values of a cubic spline;•computing the definite integral of a cubic spline.Module8.3:nag spline2d—Two-dimensional splinefittingProvides procedures for computing and evaluating spline surface approximations to arbitrary data sets in two dimensions.Procedures are available for:•generating a bicubic spline interpolant;•generating a least-squares bicubic splinefit with given interior knots;•generating a bicubic spline approximation with automatic knot placement;•computing values of a bicubic spline;•computing the definite integral of a bicubic spline.Module8.4:nag scat interp—Interpolation of scattered dataProvides procedures for computing and evaluating interpolants to scattered data sets.Procedures are available for:•generating a2-d or3-d modified Shepard interpolant;•computing values of a2-d or3-d modified Shepard interpolant,and optionally itsfirst partialderivatives.Module8.5:nag cheb1d—Chebyshev SeriesProvides procedures for computing and evaluating interpolants to1-d data sets.Procedures are available for:•finding the least-squaresfit using arbitrary data points;•generating the coefficients of the Chebyshev polynomial which interpolates(passes exactlythrough)data at a special set of points;•finding the least-squaresfit using arbitrary data points with constraints on some data points;•evaluating afitted polynomial in one variable,from Chebyshev series form;•determining the coefficients of the Chebyshev-series representing the derivatives of apolynomial in Chebyshev-series form;•determining the coefficients of the Chebyshev-series representing the indefinite integral of apolynomial in Chebyshev-series form.3Background3.1Terminology and NotationThe main aim of this chapter is to provide facilities forfitting a function of one or two variables to a given set of data points.This process will be referred to as curvefitting in the case of a single independent variable x,and surfacefitting if there are two independent variables x and y.In the curve-fitting problems considered in this chapter we have a dependent variable f and an independent variable x,and a given set of data points(x r,f r),for r=1,2,...,m.The aim is to construct a curveφ(x)which interpolates or approximates these points.For surfacefitting there is also a single dependent variable f,but there are now two independent variables x and y.The data points are denoted(x r,y r,f r),for r=1,2,...,m.In the special case where these data points lie on a rectangular mesh in the(x,y)plane the alternative notation(x q,y r,f qr),for q=1,2,...,m x,r=1,2,...,m y may be adopted.The aim is to construct a surfaceφ(x,y)which interpolates or approximates the given data set.The preliminary matters to be considered here will,for simplicity,be discussed in the context of curve-fitting problems.In fact,however,these considerations apply equally well to surface and higher-dimensional problems.Indeed,the discussion presented carries over essentially as it stands if,for these cases,we interpret x as a vector of several independent variables and correspondingly each x r as a vector containing the r th data value of each independent variable.3.2InterpolationThe process of one-dimensional interpolation may be defined as:the determination of a curveφ(x)which takes the value f r at x=x r,for r=1,2,...,m. Interpolation in higher dimensions is similarly defined.A danger with interpolation is that thefitting function may tend to exhibit unwantedfluctuations, essentially following random errors in the data and oscillating between the data points.This problem isparticularly common if thefitting function is a polynomial defined over the entire region of interest,and becomes more severe as the number of data points increases.For this reason the interpolating functions chosen in this chapter are piecewise polynomials,such as cubic splines.A cubic spline can often be used satisfactorily to interpolate a large number of data points over the whole of the data range.Unwanted fluctuations can arise,but much less frequently and much less severely than with global polynomials. An interpolating spline is not uniquely defined for a given data set,but depends on the choice made for the knots.Unwantedfluctuations may be avoided altogether by a method using piecewise cubic polynomials having onlyfirst derivative continuity.It is designed especially for monotonic data,but for other data still provides an interpolant which increases,or decreases,over the same intervals as the data.For two-dimensional interpolation the choice of procedure generally depends on the location of the data points.If these lie at the intersections of a rectangular mesh in the(x,y)plane then a bicubic spline interpolant such as nag spline2d interp in the module nag spline2d is ideal.If however the data points are arbitrarily scattered in the(x,y)plane,then nag scat2d interp from the module nag scat interp should be used instead.For three-dimensional interpolation the procedure nag scat3d interp is provided in the module nag scat interp.This interpolates a3-d scattered data set using a localized Shepard method due to Renka[2].Interpolation or approximationBefore undertaking interpolation,in other than the simplest cases,it is advisable to consider the alternative offitting the data by an approximant,which does not pass exactly through the data points, but involves significantly fewer coefficients than the corresponding interpolant.This approach is much less liable to produce unwantedfluctuations and so can often provide a better approximation to the function underlying the data.3.3ApproximationThe aim of approximation is tofit the set of data points as closely as possible with a specified function,φ(x)say,which is as smooth as possible.The requirements of smoothness and closeness conflict,however, and a balance has to be struck between them.Most often,the smoothness requirement is met simply by limiting the number of coefficients allowed in the approximating function.Given a particular number of coefficients in the function in question,the approximation procedures of this chapter generally determine the values of the coefficients such that the‘distance’of the function from the data points is as small as possible.The necessary balance should be struck by comparing a selection of such approximants having different numbers of coefficients.If the number of coefficients is too low,the approximation to the data will be poor.If the number is too high,thefit will be too close to the data,essentially following any random errors and tending to have unwantedfluctuations between the data points,as for interpolation. Between these extremes,there is often a group offits all similarly close to the data points and then the choice is clear:it is the approximant from this group having the smallest number of coefficients.The above process can be seen as the minimization of the smoothness measure(i.e.,the number of coefficients)subject to the distance from the data points being acceptably small.Some of the procedures, however,do this task themselves.They use a different measure of smoothness(in each case one that is continuous)and minimize it subject to the distance being less than a given threshold.This is a much more automatic process,requiring only some experimentation with the threshold.Fitting criteria:normsA measure of the above‘distance’between the set of data points and the functionφ(x)is needed.The distance from a single data point(x r,f r)to the function can simply be taken asr=f r−φ(x r),(1)and is called the residual of the point.However,we need a measure of distance for the set of data points as a whole.With r defined in(1),a suitable measure,or norm,ism r=1 2r,(2) which is known as the l2norm.Minimization of this norm usually provides thefitting criterion,the minimization being carried out with respect to the coefficients in the mathematical form used forφ(x).The approximant which results from minimizing(2)is the l2fit,the well known least-squares approximation.Note that minimizing(2)is equivalent to minimizing the square of(2),i.e.,the sum of squares of residuals.It is the latter which is used in practice.Strictly speaking,implicit in the use of the above norm is the statistical assumption that the random errors in the f r are independent of one another and that any errors in the x r are negligible by comparison. From this point of view,the use of the l2norm is appropriate when the random errors in the f r have a Normal distribution.Some of the procedures in this chapter do not minimize the l2norm itself,but instead minimize some (intuitively acceptable)measure of smoothness subject to the norm being less than some given threshold. These proceduresfit with cubic or bicubic splines,and the smoothing measures relate to the size of the discontinuities in their third derivatives.A much more automatic approximation algorithm follows from this approach.Weighting of data pointsThe use of the above norm also assumes that the data values f r are of equal(absolute)accuracy.Some of the procedures enable an allowance to be made to take account of differing accuracies.The allowance takes the form of‘weights’applied to the f-values so that those values known to be more accurate have a greater influence on thefit than others.These weights should be calculated from estimates of the absolute accuracies of the f-values,these estimates being expressed as standard deviations,probable errors or some other measure which has the same dimensions as f.Specifically,for each f r the corresponding weight w r should be inversely proportional to the accuracy estimate of f r.For example,if the percentage accuracy is the same for all f r,then the absolute accuracy of f r is proportional to f r(assuming f r to be positive,as it usually is in such cases)and so w r=K/f r,for r=1,2,...,m,for an arbitrary positive constant K.(This definition of weight is stressed because often weight is defined as the square of that used here.)The norm(2)above is then replaced bym r=1w2r 2r.(3) Again it is the square of(3)which is used in practice rather than(3)itself.3.4Data ConsiderationsA satisfactoryfit cannot be expected by any means if the number and arrangement of the data points do not adequately represent the character of the underlying relationship:sharp changes in behaviour,in particular,such as sharp peaks,should be well covered.Data points should extend over the whole range of interest of the independent variable(s):extrapolation outside the data ranges is most unwise.Allfits should be tested graphically before accepting them as satisfactory.For this purpose it should be noted that it is not sufficient to plot the values of thefitted function only at the data values of the independent variable(s);at the least,its values at a similar number of intermediate points should also be plotted,as unwantedfluctuations may otherwise go undetected.Such fluctuations are the less likely to occur the lower the number of coefficients chosen in thefitting function. Nofirm guide can be given,but as a rough rule,at least initially,the number of coefficients defining an approximant should not exceed half the number of data points(points with equal or nearly equal values of the independent variable,or both independent variables in surfacefitting,counting as a single point for this purpose).However,the situation may be such,particularly with a small number of data points,that a satisfactorily closefit to the data cannot be achieved without unwantedfluctuations occurring. In such cases,it is often possible to improve the situation by a transformation of one or more of the variables,as discussed in the next paragraph;otherwise it will be necessary to provide extra data points. Further advice on curvefitting is given in Cox and Hayes[1].Much of the advice applies also to surface fitting;see also the module documents.3.5Transformation of VariablesBefore starting thefitting,consideration should be given to the choice of a good form in which to deal with each of the variables:often it will be satisfactory to use the variables as they stand,but sometimes the use of the logarithm,square root,or some other function of a variable will lead to a better behaved relationship.This question is customarily taken into account in preparing graphs and tables of a relationship and the same considerations apply when curve or surfacefitting.The practical context will often give a guide.In general,it is best to avoid having to deal with a relationship whose behaviour in one region is radically different from that in another.A steep rise at the left-hand end of a curve, for example,can often best be treated by curvefitting in terms of log(x+c)with some suitable value of the constant c.According to the features exhibited in any particular case,transformation of either dependent variable or independent variable(s)or both may be beneficial.When there is a choice it is usually better to transform the independent variable(s):if the dependent variable is transformed,any weights associated with the data points must be adjusted.Thus if the f r to befitted have been obtained by a transformation f=g(F)from original data values F r,with weights W r,for r=1,2,...,m,we must takew r=W r/(d f/dF),(4) where the derivative is evaluated at F r.Strictly,the transformation of F and the adjustment of weights are valid only when the data errors in the F r are small compared with the range spanned by the F r,but this is usually the case.4References[1]Cox M G and Hayes J G(1973)Curvefitting:A guide and suite of algorithms for the non-specialistuser NPL Report NAC26National Physical Laboratory[2]Renka R J(1988)Multivariate interpolation of large sets of scattered data ACM Trans.Math.Software14139–148。

基于六角像素的图像双三次插值算法摘要与传统的方形网格相比，基于六角网格的数字图像处理方法有它独特的优点，因此，基于六角像素的图像处理技术的研究越来越受到人们的关注。

然而，由于没有成熟的硬件来支持基于六角网格下图像的获取和显示，人们的研究工作往往在模拟六角网格进行。

在四角像素中，双三次插值算法是一种插值效果较好的方法。

本文的主要任务就是研究在六角像素下的双三次插值算法的使用和使用效果。

试图证明：在六角像素下双三次插值算法也同样具有更好的插值效果。

本文采用一种Pseudo六角像素模拟方法中关于虚拟六角像素的SA算法，在虚拟六角像素定址的基础上实现虚拟六角网格中的插值实验。

具体步骤：1.首先将一个正方形像素细分为7×7的49个小像素，用双线性插值算法求每个小像素的灰度，并表示图像。

2.在虚拟的六角结构下运用双线性插值算法对灰度图像进行灰度重建，再采用双三次插值算法，对相同的灰度图像进行灰度重建。

本文采用三次卷积公式进行双三次插值。

3.返回到四角结构下显示重建图像，比较两个重建灰度图的重建效果。

4.通过计算原始图像信号－噪音功率比和最终图像的信号－噪音功率比，对实验结果进行分析比较，我们可以得到这样的结论：在六角形象素下的图像双三次插值算法同样具有更好的插值效果。

关键词：六角网格，灰度值，双三次插值精品文档你我共享Image Bicubic Interpolation AlgorithmBase on Hexagonal GridAbstractCompared to the traditional square grid,The way of image processing based on the hexangular grid has its special advantage.Therefore,people pay more and more attention to the study of image processing techlnique.However,Because there is no mature hardware supporting for the capture and display of hexagonal-based image,the study work of researchers is done based on hexangular grid imitation.Bicubic interpolation is a way in square grid which has better effect of image interpolation.The main job of this paper. is studying how to use Bicubic interpolation on the hexangular pixel and the effect of using.Try to prove that Bicubic interpolation also has better effect of image interpolation on hexangular pixel.This paper uses SA algorithm about virtual hexangular pixel which is a part of Pseudo hexangular pixel imitation,,it uses the SA algorithm to implement the virtual hexangular grid based on ascertaining the address in imitating the hexangular pixel. Concrete step:1. First,each one pixel is divided delicately to 49 small pixel. Then, we adoptthe Blinear interpolation to calculate the grey and figure the image.2. We adopt the improved Blinear interpolation based on hexangular gridimitation to reconstruct the grey image. We do it again using the improvedBicubic interpolation instead and reconstruct the same grey image. Thispaper adopts Bicubic interpolation in the use of cubic convolution formula.3. We compare the rebuilding effect of two grey images after displaying thereconstructed image on square grid.4. After computing signal to noise between original and final image andanalysing,comparing the result, we can make the conclusion that the imageBicubic interpolation based on hexangular grid has better effect ininterpolationKey Words: hexagonal grid, grey value,bicubic-interpolation目录摘要 (I)Abstract ........................................................... I I 第一章绪论 (1)1.1 研究背景 (1)1.2 研究的主要内容 (1)1.3 研究的目的意义 (2)第二章虚拟六角结构分析 (3)2.1四角网格 (3)2.2六角网格 (3)2.3六角网格的特点 (4)2.3.1四角网格与六角网格的进一步比较 (4)2.3.2六角网格的优点 (4)2.4 模拟六角网格 (5)2.3.1四角像素错位模拟六角像素 (5)2.3.2另一种方法的模拟六角结构 (6)2.3.3 Pseudo六角像素 (7)2.3.4虚拟六角结构下的图像处理 (8)第三章插值实验设计 (9)3.1 灰度插值算法 (9)3.1.1 最近邻插值算法（近邻取样法） (9)3.1.2 双线性插值法 (9)3.1.3 双三次插值法 (10)3.2 实验的软硬件条件 (11)3.2.1 实验的硬件要求 (11)3.2.2 实验的软件要求 (11)3.3 定址方法 (11)3.4基于六角网格的双线性插值实验 (13)3.5基于六角网格的双三次插值实验 (16)3.5.1传统的双三次插值算法 (16)3.5.2 改进后的基于六角网格的双三次插值算法 (16)3.5.3 实现基于六角网格的双三次插值法 (17)第四章实验结果及分析 (19)4.1 实验结果 (19)4.2 结果分析 (20)结论 (22)谢辞 (23)参考文献 (24)第一章绪论1.1 研究背景插值算法是计算机图形学和图像处理的基本算法，它广泛地应用在图像缩放和旋转、动画中间帧的生成等图形学和图像处理问题的研究之中。

航天返回与遥感第44卷第6期130 SPACECRAFT RECOVERY & REMOTE SENSING2023年12月基于单像素成像的遥感图像分辨率增强模型陈瑞林章博段熙锴孙鸣捷*（北京航空航天大学仪器科学与光电工程学院，北京100191）摘要目前对地遥感的最主要途径之一便是通过遥感相机获得目标物信息，然而遥感相机的分辨率直接影响成像质量。

结合遥感相机的推扫式成像技术，文章提出了一种基于单像素成像的超分辨增强技术模型，该模型能够简化重建过程，其设计目标是基于单像素超分辨的技术手段将航天遥感相机的图像分辨率增强4倍。

为了验证该设计思想及其重建效果，文章设置了超分辨增强仿真试验，最终仿真试验结果表明，基于单像素的超分辨模型可以将图像的信噪比提高1.1倍，且重建的图像具有明显的抑制噪声的效果，起到了良好的降噪功能，相较于其他传统图像分辨率增强方法（如双三次内插、超深超分辨神经网络）具有更高的优越性。

该方法可为地理遥感探测、土地资源探查与管理、气象观测与预测、目标毁伤情况实时评估等诸多领域的图像处理和应用提供有力支持。

关键词单像素超分辨分辨率增强推扫式成像降噪效果遥感应用中图分类号: TP751.2文献标志码: A 文章编号: 1009-8518(2023)06-0130-10 DOI: 10.3969/j.issn.1009-8518.2023.06.012Remote Sensing Image Resolution Enhancement Technology Based onSingle-Pixel ImagingCHEN Ruilin ZHANG Bo DUAN Xikai SUN Mingjie*（School of Instrument Science and Optoelectronics Engineering, Beijing University of Aeronautics and Astronautics,Beijing 100191, China）Abstract At present, one of the most important ways of earth remote sensing is to obtain target information through remote sensing cameras, but the resolution of remote sensing cameras directly affects the imaging quality. Combined with the pushbroom imaging technology of remote sensing camera, this paper proposes a super-resolution enhancement technology model based on single-pixel imaging, which can simplify the reconstruction process, and its design goal is to enhance the image resolution of aerospace remote sensing camera by 4 times based on single-pixel super-resolution technology. In order to verify the design idea and its reconstruction effect, the super-resolution enhancement simulation experiment is set up, and the final simulation results show that the single-pixel super-resolution model can improve the signal-to-noise ratio of the image by 1.1 times, and the reconstructed image has the obvious effect of suppressing noise, which plays a good noise reduction function, and has higher superiority than other收稿日期：2023-06-30基金项目：国家自然科学基金委项目（U21B2034）引用格式：陈瑞林, 章博, 段熙锴, 等. 基于单像素成像的遥感图像分辨率增强模型[J]. 航天返回与遥感, 2023, 44(6): 130-139.CHEN Ruilin, ZHANG Bo, DUAN Xikai, et al. Remote Sensing Image Resolution Enhancement Technology Based on Single-Pixel Imaging[J]. Spacecraft Recovery & Remote Sensing, 2023, 44(6): 130-139. (in Chinese)第6期陈瑞林等: 基于单像素成像的遥感图像分辨率增强模型 131traditional image resolution enhancement methods (such as bicubic interpolation and ultra-deep super-resolution neural network). This method can provide strong support for image processing and application in many fields, such as geographic remote sensing detection, land resources exploration and management, meteorological observation and prediction, and real-time assessment of target damage.Keywords single-pixel super-resolution; resolution enhancement; push-broom imaging; noise reduction effect; remote sensing application0 引言对地遥感成像的主要途径之一就是航天遥感相机，由于其具有覆盖范围广、成像速度快、风险低等优势，在国土资源管理、气象预报、地理测绘等领域发挥着举足轻重的作用。

放大照片作文英语Title: The Art of Photo Enlargement。

In the age of digital photography, the ability to enlarge photos has become an essential skill for photographers and enthusiasts alike. Whether it's for printing large-format prints or simply for enhancing details, the process of enlarging photos requires both technical know-how and artistic sensibility.Firstly, let's delve into the technical aspects of photo enlargement. When scaling up an image, one must consider the resolution and pixel density. Increasing the size of an image without maintaining an adequate resolution can result in a loss of detail and pixelation, diminishing the overall quality of the photo. Therefore, utilizing software or tools that employ algorithms to interpolate additional pixels can help mitigate these issues, ensuring a smoother enlargement process.Moreover, understanding the principles of image interpolation is crucial. Interpolation algorithms work by analyzing neighboring pixels and generating new ones tofill in the gaps when enlarging an image. Common interpolation methods include bilinear and bicubic interpolation, each with its advantages and drawbacks. Bilinear interpolation, for instance, is faster but may produce softer results, while bicubic interpolation tends to yield sharper and more accurate enlargements at the cost of processing time.However, technical proficiency alone does not guarantee a successful photo enlargement. Artistic judgment plays a significant role in determining how an enlarged photo will look and feel. It involves considering factors such as composition, lighting, and the intended emotional impact of the final image.Compositionally, one must assess how the enlarged photo will balance its elements and draw the viewer's attention. Adjustments may be necessary to crop or reframe the image to maintain its visual coherence and appeal. Additionally,paying attention to lighting and contrast can enhance the depth and dimensionality of the enlarged photo, breathing life into the subjects captured within it.Furthermore, understanding the emotional resonance of the photo is crucial. Enlarging a photo can magnify its impact, intensifying the emotions it evokes in the viewer. Whether it's a portrait conveying vulnerability, a landscape instilling a sense of awe, or a still life capturing fleeting beauty, the enlargement process should amplify these emotional nuances, inviting viewers to immerse themselves in the captured moment.Beyond technical and artistic considerations, ethical concerns also come into play when enlarging photos. In an era of digital manipulation, maintaining the authenticity and integrity of the original image is paramount. While enhancements and alterations may be made to improve visual appeal, they should not distort the truth or misrepresent reality.In conclusion, the art of photo enlargement encompassesboth technical expertise and artistic vision. By mastering the intricacies of resolution, interpolation, and composition, photographers can breathe new life into their images, transforming them into compelling works of art that resonate with viewers on a profound level. Through a delicate balance of skill and creativity, photo enlargement becomes not just a process, but a journey of discovery and expression.。

图像插值算法及其实现sensor、codec、display device都是基于pixel的，⾼分辨率图像能呈现更多的detail，由于sensor制造和chip的限制，我们需要⽤到图像插值（scaler/resize）技术，这种⽅法代价⼩，使⽤⽅便。

同时，该技术还可以放⼤⽤户希望看到的感兴趣区域。

图像缩放算法往往基于插值实现，常见的图像插值算法包括最近邻插值（Nearest-neighbor）、双线性插值（Bilinear）、双⽴⽅插值（bicubic）、lanczos插值、⽅向插值（Edge-directed interpolation）、example-based插值、深度学习等算法。

插值缩放的原理是基于⽬标分辨率中的点，将其按照缩放关系对应到源图像中，寻找源图像中的点（不⼀定是整像素点），然后通过源图像中的相关点插值得到⽬标点。

本篇⽂章，我们介绍Nearest-neighbor和Bilinear插值的原理及C实现。

插值算法原理如下：1. Nearest-neighbor最近邻插值，是指将⽬标图像中的点，对应到源图像中后，找到最相邻的整数点，作为插值后的输出。

如下图所⽰，P为⽬标图像对应到源图像中的点，Q11、Q12、Q21、Q22是P点周围4个整数点，Q12与P离的最近，因此P点的值等于Q12的值。

这⾥写图⽚描述由于图像中像素具有邻域相关性，因此，⽤这种拷贝的⽅法会产⽣明显的锯齿。

2. Bilinear双线性插值使⽤周围4个点插值得到输出，双线性插值，是指在xy⽅法上，都是基于线性距离来插值的。

如图1，⽬标图像中的⼀点对应到源图像中点P(x,y)，我们先在x⽅向插值：然后，进⾏y⽅向插值：可以验证，先进⾏y⽅向插值再进⾏x⽅向插值，结果也是⼀样的。

值得⼀提的是，双线性插值在单个⽅向上是线性的，但对整幅图像来说是⾮线性的。

3. C实现使⽤VS2010，⼯程包含三个⽂件，如下：main.cpp#include <string.h>#include <iostream>#include "resize.h"int main(){const char *input_file = "D:\\simuTest\\teststream\\00_YUV_data\\01_DIT_title\\data.yuv"; //absolute pathconst char *output_file = "D:\\simuTest\\teststream\\00_YUV_data\\01_DIT_title\\data_out2.yuv"; //absolute pathint src_width = 720;int src_height = 480;int dst_width = 1920;int dst_height = 1080;int resize_type = 1; //0:nearest, 1:bilinearresize(input_file, src_width, src_height, output_file, dst_width, dst_height, resize_type);return 0;}resize.cpp#include "resize.h"int clip3(int data, int min, int max){return (data > max) ? max : ((data < min) ? min : data);if(data > max)return max;else if(data > min)return data;elsereturn min;}//bilinear takes 4 pixels (2×2) into account/** 函数名： bilinearHorScaler* 说明：⽔平⽅向双线性插值* 参数：*/void bilinearHorScaler(int *src_image, int *dst_image, int src_width, int src_height, int dst_width, int dst_height){double resizeX = (double)dst_width / src_width;for(int ver = 0; ver < dst_height; ++ver){for(int hor = 0; hor < dst_width; ++hor){double srcCoorX = hor / resizeX;double weight1 = srcCoorX - (double)((int)srcCoorX);double weight2 = (double)((int)(srcCoorX + 1)) - srcCoorX;double dstValue = *(src_image + src_width * ver + clip3((int)srcCoorX, 0, src_width - 1)) * weight2 + *(src_image + src_width * ver + clip3((int)(srcCoorX + 1), 0, src_width - 1)) * weight1; *(dst_image + dst_width * ver + hor) = clip3((uint8)dstValue, 0, 255);}}}/** 函数名： bilinearVerScaler* 说明：垂直⽅向双线性插值* 参数：*/void bilinearVerScaler(int *src_image, int *dst_image, int src_width, int src_height, int dst_width, int dst_height){double resizeY = (double)dst_height / src_height;for(int ver = 0; ver < dst_height; ++ver){for(int hor = 0; hor < dst_width; ++hor){double srcCoorY = ver / resizeY;double weight1 = srcCoorY - (double)((int)srcCoorY);double weight2 = (double)((int)(srcCoorY + 1)) - srcCoorY;double dstValue = *(src_image + src_width * clip3((int)srcCoorY, 0, src_height - 1) + hor) * weight2 + *(src_image + src_width * clip3((int)(srcCoorY + 1), 0, src_height - 1) + hor) * weight1; *(dst_image + dst_width * ver + hor) = clip3((uint8)dstValue, 0, 255);}}}/** 函数名： yuv420p_NearestScaler* 说明：最近邻插值* 参数：*/void nearestScaler(int *src_image, int *dst_image, int src_width, int src_height, int dst_width, int dst_height){double resizeX = (double)dst_width /src_width; //⽔平缩放系数double resizeY = (double)dst_height / src_height; //垂直缩放系数int srcX = 0;int srcY = 0;for(int ver = 0; ver < dst_height; ++ver) {for(int hor = 0; hor < dst_width; ++hor) {srcX = clip3(int(hor/resizeX + 0.5), 0, src_width - 1);srcY = clip3(int(ver/resizeY + 0.5), 0, src_height - 1);*(dst_image + dst_width * ver + hor) = *(src_image + src_width * srcY + srcX);}}}void resize(const char *input_file, int src_width, int src_height, const char *output_file, int dst_width, int dst_height, int resize_type){//define and init src bufferint *src_y = new int[src_width * src_height];int *src_cb = new int[src_width * src_height / 4];int *src_cr = new int[src_width * src_height / 4];memset(src_y, 0, sizeof(int) * src_width * src_height);memset(src_cb, 0, sizeof(int) * src_width * src_height / 4);memset(src_cr, 0, sizeof(int) * src_width * src_height / 4);//define and init dst bufferint *dst_y = new int[dst_width * dst_height];int *dst_cb = new int[dst_width * dst_height / 4];int *dst_cr = new int[dst_width * dst_height / 4];memset(dst_y, 0, sizeof(int) * dst_width * dst_height);memset(dst_cb, 0, sizeof(int) * dst_width * dst_height / 4);memset(dst_cr, 0, sizeof(int) * dst_width * dst_height / 4);//define and init mid bufferint *mid_y = new int[dst_width * src_height];int *mid_cb = new int[dst_width * src_height / 4];int *mid_cr = new int[dst_width * src_height / 4];memset(mid_y, 0, sizeof(int) * dst_width * src_height);memset(mid_cb, 0, sizeof(int) * dst_width * src_height / 4);memset(mid_cr, 0, sizeof(int) * dst_width * src_height / 4);uint8 *data_in_8bit = new uint8[src_width * src_height * 3 / 2];memset(data_in_8bit, 0, sizeof(uint8) * src_width * src_height * 3 / 2);uint8 *data_out_8bit = new uint8[dst_width * dst_height * 3 / 2];memset(data_out_8bit, 0, sizeof(uint8) * dst_width * dst_height * 3 / 2);FILE *fp_in = fopen(input_file,"rb");if(NULL == fp_in){//exit(0);printf("open file failure");}FILE *fp_out = fopen(output_file, "wb+");//data readfread(data_in_8bit, sizeof(uint8), src_width * src_height * 3 / 2, fp_in);//Y componentfor(int ver = 0; ver < src_height; ver++){for(int hor =0; hor < src_width; hor++){src_y[ver * src_width + hor] = data_in_8bit[ver * src_width + hor];}}//c component YUV420Pfor(int ver = 0; ver < src_height / 2; ver++){for(int hor =0; hor < src_width / 2; hor++){src_cb[ver * (src_width / 2) + hor] = data_in_8bit[src_height * src_width + ver * src_width / 2 + hor];src_cr[ver * (src_width / 2) + hor] = data_in_8bit[src_height * src_width + src_height * src_width / 4 + ver * src_width / 2 + hor];}}//resizeif(0 == resize_type){nearestScaler(src_y, dst_y, src_width, src_height, dst_width, dst_height);nearestScaler(src_cb, dst_cb, src_width / 2, src_height / 2, dst_width / 2, dst_height / 2);nearestScaler(src_cr, dst_cr, src_width / 2, src_height / 2, dst_width / 2, dst_height / 2);}else if(1 == resize_type){bilinearHorScaler(src_y, mid_y, src_width, src_height, dst_width, src_height);bilinearHorScaler(src_cb, mid_cb, src_width / 2, src_height / 2, dst_width / 2, src_height / 2);bilinearHorScaler(src_cr, mid_cr, src_width / 2, src_height / 2, dst_width / 2, src_height / 2);bilinearVerScaler(mid_y, dst_y, dst_width, src_height, dst_width, dst_height);bilinearVerScaler(mid_cb, dst_cb, dst_width / 2, src_height / 2, dst_width / 2, dst_height / 2);bilinearVerScaler(mid_cr, dst_cr, dst_width / 2, src_height / 2, dst_width / 2, dst_height / 2);}else{nearestScaler(src_y, dst_y, src_width, src_height, dst_width, dst_height);nearestScaler(src_cb, dst_cb, src_width / 2, src_height / 2, dst_width / 2, dst_height / 2);nearestScaler(src_cr, dst_cr, src_width / 2, src_height / 2, dst_width / 2, dst_height / 2);}//data writefor(int ver = 0; ver < dst_height; ver++){for(int hor =0; hor < dst_width; hor++){data_out_8bit[ver * dst_width + hor] = clip3(dst_y[ver * dst_width + hor], 0, 255);}}for(int ver = 0; ver < dst_height / 2; ver++){for(int hor = 0; hor < dst_width / 2; hor++){data_out_8bit[dst_height * dst_width + ver * dst_width / 2 + hor] = clip3(dst_cb[ver * (dst_width / 2) + hor], 0, 255);data_out_8bit[dst_height * dst_width + dst_height * dst_width / 4 + ver * dst_width / 2 + hor] = clip3(dst_cr[ver * (dst_width / 2) + hor], 0, 255); }}fwrite(data_out_8bit, sizeof(uint8), dst_width * dst_height * 3 / 2, fp_out);delete [] src_y;delete [] src_cb;delete [] src_cr;delete [] dst_y;delete [] dst_cb;delete [] dst_cr;delete [] mid_y;delete [] mid_cb;delete [] mid_cr;delete [] data_in_8bit;delete [] data_out_8bit;fclose(fp_in);fclose(fp_out);}resize.h#ifndef RESIZE_H#define RESIZE_H#include <stdio.h>#include <string.h>typedef unsigned char uint8;typedef unsigned short uint16;int clip3(int data, int min, int max);void bilinearHorScaler(int *src_image, int *dst_image, int src_width, int src_height, int dst_width, int dst_height);void bilinearVerScaler(int *src_image, int *dst_image, int src_width, int src_height, int dst_width, int dst_height);void nearestScaler(int *src_image, int *dst_image, int src_width, int src_height, int dst_width, int dst_height);void resize(const char *input_file, int src_width, int src_height, const char *output_file, int dst_width, int dst_height, int resize_type);#endif效果⽐较将720x480分辨率图像放⼤到1080p，1：1截取局部画⾯如下，左边是最近邻放⼤的效果，右边是双线性效果，可以看到，双线性放⼤的锯齿要明显⽐最近邻⼩。

DOI：10.19368/ki.2096-1782.2023.03.115双歧杆菌乳杆菌三联活菌联合改良序贯疗法在合并Hp感染慢性萎缩性胃炎中的应用石建祥泰兴市第三人民医院消化内科，江苏泰兴225400[摘要]目的研究合并幽门螺杆菌（helicobacter pylori, Hp）感染的慢性萎缩性胃炎治疗中联合应用改良序贯疗法与双歧杆菌乳杆菌三联活菌的效果。

方法采用奇偶数分组法将2020年9月—2021年9月泰兴市第三人民医院收治的60例合并Hp感染慢性萎缩性胃炎患者分为两组，对照组（30例）采用改良序贯疗法治疗，研究组（30例）采用改良序贯疗法与双歧杆菌乳杆菌三联活菌治疗。

观察评估两组Hp根除效果、临床治疗效果、炎症反应情况及不良反应发生情况。

结果研究组Hp根除率、治疗总有效率分别为93.33%、96.67%，高于对照组的Hp根除率（70.00%）、治疗总有效率（73.33%），差异有统计学意义（χ2=5.455、4.706，P=0.020、0.030）。

治疗后研究组TNF-α、CRP及IL-6水平分别为（1.89±0.21）mg/L、（11.96±1.25）ng/L、（30.36±3.02）ng/L，低于对照组的（2.41±0.38）mg/L、（17.64±2.20）ng/L、（37.77±3.85）ng/L，差异有统计学意义（t=6.560、12.295、8.295，P<0.05）。

研究组不良反应发生率为10.00%，与对照组的26.67%对比，差异无统计学意义（χ2= 2.783，P=0.095）。

结论针对合并Hp感染慢性萎缩性胃炎患者，联合应用改良序贯疗法与双歧杆菌乳杆菌三联活菌治疗的疗效更佳，可有效根除Hp，减轻机体炎症反应，且安全性较高。

[关键词]慢性萎缩性胃炎；幽门螺杆菌；益生菌；序贯疗法；不良反应[中图分类号]R521 [文献标识码]A [文章编号]2096-1782（2023）02(a)-0115-04Application of Bifidobacterium Lactobacillus Triple Live Bacteria Com⁃bined with Improved Sequential Therapy in Chronic Atrophic Gastritis Complicated with HpSHI JianxiangDepartment of Gastroenterology, Taixing Third People′s Hospital, Taixing, Jiangsu Province, 225400 China[Abstract] Objective To investigate the effect of combined improved sequential therapy and bifidobacterium lactoba⁃cillus triple live bacteria in the treatment of chronic atrophic gastritis infected with helicobacter pylori (Hp). Methods Using odd-even number grouping method, 60 patients with chronic atrophic gastritis complicated with Hp infection ad⁃mitted to the Third People′s Hospital of Taixing City from September 2020 to September 2021 were divided into two groups. The control group (30 cases) was treated with improved sequential therapy, and the study group (30 cases) was treated with improved sequential therapy and bifidobacterium lactobacillus triple live bacteria. Observed and evalu⁃ated the Hp eradication effect, clinical treatment effect, inflammatory reaction and adverse reaction of the two groups.Results The Hp eradication rate and the total effective rate of treatment in the study group were 93.33% and 96.67% respectively, which were higher than those in the control group (70.00%) and the total effective rate of treatment (73.33%), and the difference was statistically significant (χ2=5.455, 4.706, P=0.020, 0.030). After treatment, the levels of TNF-α, CRP and IL-6 in the study group were (1.89±0.21) mg/L, (11.96±1.25) ng/L, (30.36±3.02) ng/L, respec⁃tively, lower than those in the control group (2.41±0.38) mg/L, (17.64±2.20) ng/L, (37.77±3.85) ng/L, and the differ⁃ence was statistically significant (t=6.560, 12.295, 8.295, P<0.05). The incidence of adverse reactions in the study group was 10.00%, and there was no statistically significant difference compared with 26.67% in the control group (χ2=[作者简介] 石建祥（1975-），男，本科，副主任医师，研究方向为消化内科。

NMR 中常用的英文缩写和中文名称收集了一些NMR 中常用的英文缩写,译出其中文名称,供初学者参考,不妥之处请指出,也请继续添加.相关附件NMR 中常用的英文缩写和中文名称APT Attached Proton Test 质子连接实验ASIS Aromatic Solvent Induced Shift 芳香溶剂诱导位移BBDR Broad Band Double Resonance 宽带双共振BIRD Bilinear Rotation Decoupling 双线性旋转去偶(脉冲)COLOC Correlated Spectroscopy for Long Range Coupling 远程偶合相关谱COSY ( Homonuclear chemical shift ) COrrelation SpectroscopY (同核化学位移)相关谱CP Cross Polarization 交叉极化CP/MAS Cross Polarization / Magic Angle Spinning 交叉极化魔角自旋CSA Chemical Shift Anisotropy 化学位移各向异性CSCM Chemical Shift Correlation Map 化学位移相关图CW continuous wave 连续波DD Dipole-Dipole 偶极-偶极DECSY Double-quantum Echo Correlated Spectroscopy 双量子回波相关谱DEPT Distortionless Enhancement by Polarization Transfer 无畸变极化转移增强2DFTS two Dimensional FT Spectroscopy 二维傅立叶变换谱DNMR Dynamic NMR 动态NMRDNP Dynamic Nuclear Polarization 动态核极化DQ(C) Double Quantum (Coherence) 双量子(相干)DQD Digital Quadrature Detection 数字正交检测DQF Double Quantum Filter 双量子滤波DQF-COSY Double Quantum Filtered COSY 双量子滤波COSYDRDS Double Resonance Difference Spectroscopy 双共振差谱EXSY Exchange Spectroscopy 交换谱FFT Fast Fourier Transformation 快速傅立叶变换FID Free Induction Decay 自由诱导衰减H,C-COSY 1H,13C chemical-shift COrrelation SpectroscopY 1H,13C 化学位移相关谱H,X-COSY 1H,X-nucleus chemical-shift COrrelation SpectroscopY 1H,X- 核化学位移相关谱HETCOR Heteronuclear Correlation Spectroscopy 异核相关谱HMBC Heteronuclear Multiple-Bond Correlation 异核多键相关HMQC Heteronuclear Multiple Quantum Coherence 异核多量子相干HOESY Heteronuclear Overhauser Effect Spectroscopy 异核Overhause 效应谱HOHAHA Homonuclear Hartmann-Hahn spectroscopy 同核Hartmann-Hahn 谱HR High Resolution 高分辨HSQC Heteronuclear Single Quantum Coherence 异核单量子相干INADEQUATE Incredible Natural Abundance Double Quantum Transfer Experiment 稀核双量子转移实验（简称双量子实验，或双量子谱）INDOR Internuclear Double Resonance 核间双共振INEPT Insensitive Nuclei Enhanced by Polarization 非灵敏核极化转移增强INVERSE H,X correlation via 1H detection 检测1H 的H,X 核相关IR Inversion-Recovery 反（翻）转回复JRES J-resolved spectroscopy J-分解谱LIS Lanthanide （chemical shift reagent ） Induced Shift 镧系（化学位移试剂）诱导位移LSR Lanthanide Shift Reagent 镧系位移试剂MAS Magic-Angle Spinning 魔角自旋MQ（C）Multiple-Quantum （ Coherence ）多量子（相干）MQF Multiple-Quantum Filter 多量子滤波MQMAS Multiple-Quantum Magic-Angle Spinning 多量子魔角自旋MQS Multi Quantum Spectroscopy 多量子谱NMR Nuclear Magnetic Resonance 核磁共振NOE Nuclear Overhauser Effect 核Overhauser 效应（NOE）NOESY Nuclear Overhauser Effect Spectroscopy 二维NOE 谱NQR Nuclear Quadrupole Resonance 核四极共振PFG Pulsed Gradient Field 脉冲梯度场PGSE Pulsed Gradient Spin Echo 脉冲梯度自旋回波PRFT Partially Relaxed Fourier Transform 部分弛豫傅立叶变换PSD Phase-sensitive Detection 相敏检测PW Pulse Width 脉宽RCT Relayed Coherence Transfer 接力相干转移RECSY Multistep Relayed Coherence Spectroscopy 多步接力相干谱REDOR Rotational Echo Double Resonance 旋转回波双共振RELAY Relayed Correlation Spectroscopy 接力相关谱RF Radio Frequency 射频ROESY Rotating Frame Overhauser Effect Spectroscopy 旋转坐标系NOE 谱ROTO ROESY-TOCSY Relay ROESY-TOCSY 接力谱SC Scalar Coupling 标量偶合SDDS Spin Decoupling Difference Spectroscopy 自旋去偶差谱SE Spin Echo 自旋回波SECSY Spin-Echo Correlated Spectroscopy 自旋回波相关谱SEDOR Spin Echo Double Resonance 自旋回波双共振SEFT Spin-Echo Fourier Tran sform Spectroscopy （with J modulati on）（J-调制）自旋回波傅立叶变换谱SELINCOR SELINQUATE SFORD SNR or S/NSelective Inverse Correlation 选择性反相关Selective INADEQUA TE 选择性双量子（实验）Single Frequency Off-Resonance Decoupling 单频偏共振去偶Signal-to-noise Ratio 信/ 燥比SQF Single-Quantum Filter 单量子滤波SRTCF TOCSY TORO TQF WALTZ-16 Saturation-Recovery 饱和恢复Time Correlation Function 时间相关涵数Total Correlation Spectroscopy 全(总)相关谱TOCSY-ROESY Relay TOCSY-ROESY 接力Triple-Quantum Filter 三量子滤波A broadband decoupling sequence 宽带去偶序列WATERGATE Water suppression pulse sequence 水峰压制脉冲序列WEFTZQ(C) ZQF T1T2 tmWater Eliminated Fourier Transform 水峰消除傅立叶变换Zero-Quantum (Coherence) 零量子相干Zero-Quantum Filter 零量子滤波Longitudinal (spin-lattice) relaxation time for MZ 纵向(自旋- 晶格)弛豫时间Transverse (spin-spin) relaxation time for Mxy 横向(自旋-自旋)弛豫时间T C rotational correlation time 旋转相关时间。

关于Entrez与SRA，一点小技巧今天是生信星球陪你的第231天大神一句话，菜鸟跑半年。

我不是大神，但我可以缩短你走弯路的半年~就像歌儿唱的那样，如果你不知道该往哪儿走，就留在这学点生信好不好~这里有豆豆和花花的学习历程，从新手到进阶，生信路上有你有我！刘小泽写于2018.12.27首先关于昨天写的推送简单了解下热门的明星基因们，有个基因名有错误“BRAC”应该是“BRCA”（基因名写错实属不应该啊 ）今天介绍的原文来自Biostar handbook。

NCBI应该是最常用到的数据库了，其中的Entrez数据库作为一个一级数据库，整合了PubMed和DNA、蛋白的序列、基因、结构、变异、基因表达等信息。

因为数据量实在是太大了，因此我们必须了解怎么获取、下载数据。

简介Entrez是一个法语词汇，我们一般称之为“en-trez”，为了方便获取其中的数据，NCBI提供了一个Entrez E-utils的web API，不过这个使用比较麻烦；另外，命令行的下载工具Entrez Direct 是经常使用的，简化了下载流程。

/books/NBK179288//p/92671/看一下Entrez的基础搜索我们一般搜索序列是怎么搜索的呢？比如我们要搜索Ebola virus1976，结果返回Ebola病毒的全基因组信息（/nuccore/AF086833.2），对于一条序列整个过程就是这么简单注意到：accession number是AF086833，version number是AF086833.2 。

第一个即便序列日后再做改动，它的编号还是保持不变；第二个随着修改版本而修改小数点后的版本号另外之前还有一种索引号叫GI编号，但是NCBI自从2015年以后对于新加的序列都取消了这个编号信息如何使用Entrez Direct？最常用到的命令就是`efetch`#得到Genbank序列efetch -db=nuccore -format=gb -id=AF086833 >AF086833.gb#得到fasta序列efetch -db=nuccore -format=fasta -id=AF086833 >AF086833.fa#还可以选取其中一段序列efetch -db=nuccore -format=fasta -id=AF086833 -seq_start=1 -seq_stop=3当然，如果序列多的话，直接用循环就好另外还可以指定正负链#指定正链efetch -db=nuccore -format=fasta -id=AF086833 -seq_start=1 -seq_stop=5 -strand=1>AF086833.2:1-5 Ebola virus - Mayinga, Zaire, 1976, complete genomeCGGAC#指定负链efetch -db=nuccore -format=fasta -id=AF086833 -seq_start=1 -seq_stop=5 -strand=2>AF086833.2:c5-1 Ebola virus - Mayinga, Zaire, 1976, complete genomeGTCCG#可以看到，第二个命令得到的结果中 >AF086833.2:c5-1，与第一个的>AF086833.2:1-5不同，说明这个是反向互补片段利用`esearch`进行搜索假如有一个项目序列号PRJNA257197，一般文章中都会提供这样的序列号，拿到它可以去下载一些信息，而不用登陆NCBI自己去找esearch -help 查看帮助信息#检索的话需要提供-db 和 -queryesearch -db nucleotide -query PRJNA257197esearch -db protein -query PRJNA257197#结果会返回像这样的“环境”信息，这个信息我们目前用不到，但是可以在其他的Entrez direct项目中可以用到(比如下面的序列获取)nucleotideNCID_1_77384293_130.14.22.215_9001_1545880173_16811 82876_0MetA0_S_MegaStore12491#想要得到相关的序列esearch -db nucleotide -query PRJNA257197 | efetch -format=fasta > genome.faesearch -db protein -query PRJNA257197 | efetch -format=fasta > protein.fa我们知道了存在这个xml文件，就可以利用它提取更多的内容efetch -db taxonomy -id 9606,7227,10090 -format xml | xtract -Pattern Taxon -first TaxId ScientificName GenbankCommonName Division #结果得到9606 Homo sapiens human Primates7227 Drosophila melanogaster fruit fly Invertebrates10090 Mus musculus house mouse Rodents如何得到多个SRA数据信息？说到SRA（Short Read Archive），你应该立刻想到原始数据都存在里面，我们处理数据的第一步也就是下载SRA文件，一般来讲，都会用到几个甚至十几个SRA原始数据，而它们的存储也是有自己的结构的。