Rate-Distortion Optimized Embedding
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脑电信号的特征提取方法胡文凤;宋江玲;张瑞【摘要】癫痫是一种常见的发病率极高的慢性脑疾病,全球约有1%的人口患有癫痫.传统的癫痫性发作检测主要依赖于临床医生对脑电图进行视觉上的检查,并结合临床经验给出诊断.但海量的脑电数据使得这一传统方法不仅十分耗时,而且主观性很强.因此,开展癫痫性发作自动检测的研究以辅助医生完成癫痫性发作检测具有重要的临床意义.而如何从脑电图中提取合适的脑电特征以及如何选取恰当的分类器是完成癫痫性发作自动检测的关键环节,其中如何从脑电图中提取出能够区别发作脑电与未发作脑电特征是首先的也是最为重要的一步.总结了三种常见的用于癫痫性发作自动检测的基于非线性相似性的脑电特征提取方法,通过分析其优缺点,给出相应的改进建议.【期刊名称】《西安文理学院学报(自然科学版)》【年(卷),期】2016(019)003【总页数】5页(P21-24,56)【关键词】癫痫;癫痫性发作;癫痫性发作的自动检测;非线性动力学;基于顺序模式的非相似性;模糊相似性指数;基于巴氏距离的非相似性【作者】胡文凤;宋江玲;张瑞【作者单位】西北大学数学学院,西安710127;西北大学数学学院,西安710127;西北大学数学学院,西安710127【正文语种】中文【中图分类】O29癫痫是一种常见的,发病率仅次于中风的第二大慢性脑疾病[1].癫痫性发作是由大脑局部区域的大量神经元超同步异常放电所产生,临床表现为短暂的感觉障碍、肢体抽搐、意识丧失、行为障碍等,严重威胁着人们的正常生活乃至生命.脑电图(electroencephalographic, EEG)是大脑电活动的记录,它蕴含着丰富的生理及病理信息[2].从生理角度来讲,不同的脑电图对应于受体不同的生理活动(如静坐、走动、跑跳等);从病理角度来讲,不同的脑电图蕴含着不同的病理信息(如癫痫、阿尔茨海默病等).传统的癫痫性发作检测主要是依靠医生对患者的脑电图进行视觉检查并结合临床症状进行综合诊断而完成.然而长时程的脑电图监测所产生的海量脑电数据,使得这一诊断方法不仅十分耗时而且主观性很强.基于传统检测方法的局限性,开展癫痫性发作自动检测技术的研究就具有重要的临床应用价值.其本质在于通过计算机技术及机器学习方法完成对脑电图的分析进而得出相应的辅助诊断结果.由于EEG中所蕴含信息的广度及深度,癫痫性发作自动检测中一个重要步骤是通过恰当的方法将EEG中隐含的癫痫病理信息提取出来,这一过程称作特征提取.将所提取的特征分配给恰当的分类器以最终完成癫痫性发作的自动检测.如何从包含思想、情绪、行为、病理等因素的脑电信号中提取出能将癫痫发作与未发作脑电区别开来的特征,是一项具有挑战性但同时至关重要的工作.这一问题自1982年癫痫性发作自动检测被首次提出之时[3],一直是学者们的研究重心.随着癫痫性发作自动检测技术的发展,大量的特征提取方法已被广泛提出.大体可以分为两类:一类是各状态下(发作与未发作)的特征值可以独立计算;另一类是各个状态的特征值是不可以独立计算.在这一情形下,我们往往需要提前设置一个参考状态,然后将所有的脑电片段与之进行相似性对比,进而根据对比结果得出特征.本文主要对非线性动力学意义下的几种刻画相似性的脑电特征提取方法进行系统阐述,通过分析其优缺点,给出相应的改进建议.1.1 非线性动力学非线性动力学是主要研究非线性动力系统(即动力系统的输出与输入满足非线性时的关系)中状态变量随时间变化情况的一门学科[4].一个系统中全部可能状态变量的集合称为状态空间或相空间,但在许多情形下,一个系统中的所有状态变量或者状态变量之间的相互关系并非已知,因此往往需要对相空间进行重构,进而通过研究重构相空间来揭示动力系统的内在变化规律.时间延迟方法是一种比较典型且常用的相空间重构方法.给定一个时间序列{Xn:n=1,2,…,Nn},矩阵A=(aij)m×N称为重构相空间(也称作信号Xn的轨迹矩阵),其中这里N=Nn-(m-1)τ是状态变量的个数,m是嵌入维数,τ是时间延迟,A中每一列为一个状态变量,即.1.2 基于顺序模式的非相似性Ouyang等人于2010年提出基于顺序模式的非相似性(ordinal pattern based dissimilarity,OPBS)的概念[5],其基本思想为:由于白噪声是一种完全随机的不包含任何信息的信号,那么对其进行顺序排列后,所有顺序模式是等概率出现的,从而所有状态变量的顺序模式也服从等概率出现.但对于包含一定信息量的信号,其状态变量的顺序模式应该是具有一定规律性,且对应不同含义信号的顺序模式应该是不同的.基于上述认知,Ouyang等人应用状态变量顺序模式的概率作为EEG的特征进行癫痫性发作自动检测.具体的算法总结如下:步骤1:将原始EEG信号X={x1,x2,…,xnn},划分为等长的脑电片段{Si:i=1,2,…,n},每一Si中均包含l个样本点,即n=Nn/l.在所有Si中随机选取一个发作脑电作为参考信号,记作Sref.为方便起见,其余所有片段均称为当前信号,并记作St.作Xt和Xref,重构得到的这两个相空间中每一列即为相应的状态变量.步骤3:分别对Xt和Xref中每一状态变量进行升序排列,得到所对应的升序模式集合Ot和Oref.由于每个状态变量由m个点组成,所以共有m!个顺序模式,记作O={O1,O2,…,Om!},其中每一Oi对应一个顺序模式.将模式Oref和Ot每一列(状态变量)与顺序模式O中所有元素的每一列进行对比,得出在顺序模式O中出现的次数,分别记作C(π)=[C(π1),C(π2),…,C(πm!)]和m!)].步骤4:分别计算当前信号和参考信号对应的升序模式的概率,记作P(π)和),其中.步骤5:定义OPBS为其中Dm∈[0,1].当Dm=1时,则表示当前信号与参考信号完全不同;当Dm=0时,则表示两个信号完全相同.其中m的选取至关重要,太大或太小都不能体现全部的顺序模式.m的选取和片段的长度l有关,满足m!+(m-1)τ≪l[6].1.3 模糊相似性指数动态相似性(dynamical similarity index,DSI)最早是用来刻画颞叶癫痫在发作前颅内脑电变化的特征提取方法.主要思想是通过对大脑不同状态下脑电信号相空间进行处理后,利用Heaviside函数计算不同状态间的相似性[7].而Heaviside函数是硬函数,即取值仅为1或0,基于此局限性,Ouyang等人提出模糊相似性的概念(fuzzy similarity index,FSI)[8],其作为DSI 的一种改进,主要是将Heaviside函数替换为高斯函数,FSI得到更多关注与应用.FSI的计算步骤如下:步骤1:从X中选择一段连续300 s长的未发作的EEG作为参考信号,记作Sref.对原始信号X进行划分,将划分结果记作S={S1,S2,…,Sn},其中Si包含l个样本点,且保证其只代表一种状态(发作或未发作),为了方便起见,我们将所有的Si 均称为当前信号,记作St.A(St)和A(Sref).步骤3:为进一步降低噪声,通过奇异值分解(singular value decomposition,SVD)将A(Sref)和A(St)分别投影到A(Sref)的主轴,得到X(Sref)和X(St).步骤4:从参考状态X(Sref)中随机抽取矩阵,记作Y(Sref),并计算这里Nref和Nt分别是状态空间A(Sref)和A(St)的点的个数.r是需要确定的参数,一般取r为参考信号的累计临界分布的30%的上分位点[9].步骤5:计算模糊相似度指数(FSI)取值在0和1之间,当越趋近于1表示越相似;当越接近于0时,则表示越不相似.1.4 基于巴氏距离的非相似性基于巴氏距离的非相似性(bhattacharyya based dissimilarity index,BBDI)是由Nikanazar于2010 年提出的一种基于FSI的改进方法[10].由于在计算FSI时需要确定参数r,而r的取值依赖于参考信号,需要在参考信号确定的基础上来进一步设定.而在BBDI中,状态空间的相似性最终由巴氏距离计算,进而避免了在FSI中参数r的选取,且该算法再无其他参数.BBDI的计算步骤如下:步骤1:从X中随机选择一段连续的时长300 s的未发作EEG作为参考信号,记作Sref.对原始信号X进行划分,将划分结果记作S={S1,S2,…,Sn},其中包含l个样本点,且只代表一种状态(发作Si或未发作).为简单起见,我们将所有的Si均称为当前信号,记作St.步骤2:利用公式(1)分别对当前信号St和参考信号Sref进行相空间重构,得到A(St)和A(Sref).步骤3:为进一步降低噪声,通过奇异值分解将A(Sref)和A(St)分别投影到A(Sref)的主轴,得到X(Sref)和X(St).步骤4:各脑电片段的统计分布的巴氏距离可表示为这里mx(St)和mx(Sref)分别表示X(St)和X(Sref)的列均值,PX(St)和PX(Sref)分别为其对应的协方差矩阵.且如果当前信号和参考信号越相似,则BBDI的值会较小;相反,BBDI的值会比较大.回顾上述所有算法,它们面临的共同问题是如何确定嵌入维数m和时间延迟τ.不同的嵌入维数和时间延迟会对算法的性能产生很大的影响,目前已有许多方法被用来确定恰当的嵌入维数和时间延迟,例如用互信息法(Mutual information,MI)[11]确定时间延迟,Cao’s法[12]确定嵌入维数等,读者可查阅相关文献[13-14].本文主要介绍了3种基于非线性相似性度量的脑电特征提取方法.OPBS是对信号顺序模式的分析,基于包含不同信息的信号顺序模式间具有差异性这一认识,研究癫痫发作与未发作状态变量的顺序模式间的非相似性,以非相似性的大小来判断癫痫发作与否.FSI是对动力系统轨迹矩阵的分析,基于不同动力系统轨迹矩阵间具有差异性的认识,研究癫痫发作与未发作情况下轨迹矩阵间的相似性,从而对癫痫发作与否进行判断.BBDI是对FSI算法的一种改进.FSI在计算相似性时会涉及高斯函数中参数r的确定,而r的取值又依赖于参考信号本身.为了避免这一问题,Nikanazar提出了基于巴氏距离的非相似性算法,即BBDI.结合以上算法的介绍,可以考虑从以下两个方面对算法进行改进:(1) 对于顺序模式,考虑从顺序模式的分布意义着手,对其分布进行统计分析,然后计算统计特征间相似性;(2)对于轨迹矩阵,可以从矩阵变换和相似性两个角度考虑进行改进.张瑞(1971—),女,陕西西安人,西北大学数学学院教授,主要从事计算智能及信息技术研究.【相关文献】[1] KUMAR T S,KANHANGAD V,PACHORI R B.Classification of seizure and seizure-free EEG signals using local binary patterns[J].Biomedical Signal Processing &Control,2015,15:33-40.[2] RAY G C.An algorithm to separate nonstationary part of a signal using mid-prediction filter[J].IEEE Transactions on Signal Processing,1994,42(9):2276-2279.[3] GOTMAN J.Automatic recognition of epileptic seizures in theEEG[J].Electroencephalography & Clinical Neurophysiology,1982,54(5):530-540.[4] 刘秉正,彭建华.非线性动力学[M].北京: 教育出版社,2004.[5] OUNYANG G X,DANG C Y,RICHARDS DA,et al.Ordinal pattern based similarity analysis for EEG recordings[J].Clinical Neurophysiology,2010,121(5):694-703.[6] AMIGO J M,KENNEL M B.Topological permutation entropy[J].Physica D Nonlinear Phenomena,2010,231(231):125-145.[7] QUYEN M L V,MATTINERIE L,NAVARRO V,et al.Adam.Anticipation of epileptic seizures from standard EEGrecordings[J].The Lancet,2001,357:183-188.[8] OUYANG G,LI X,GUAN e of fuzzy similarity index for epileptic seizure prediction[C].The 5th World Congress on Intelligent Control andAutomation.Hangzhou,China,2004 June; 14-18:5351-5535.[9] QUYEN M,ADAM C,MARTINERIE J,et al.Spatiotemporal characterization of non-linear changes in intracranial activities prior to human temporal lobe seizures[J].European Journal of Neuroscience,2000,12:2124-2134.[10]NIKNAZAR M,MOUSAVI S R,VOSOUGHI V B,et al.A new dissimilarity index on EEG signals for epileptic seizure detection[C].4th International Symposium on Communications,Control and Signal Processing (ISCCSP 2010) 2010: 1-5.[11]FRASER A M,SWINNEY H L.Independent Coordinates for Strange Attractors from Mutual Information[J].Physical Review A,1986,33(2):1134-1140.[12]CAO L.Practical method for determining the minimum embedding dimension of a scalar time series[J].Physica D: Nonlinear Phenomena,1997,110(1):43-50.[13]王红礼,张琪昌,郭树起,等.非线性动力学理论及其应用[M].天津: 天津科学技术出版社,2002.[14]SONG Y D,CROWCROFT J,ZHANG J X.Automatic epileptic seizure detection in EEGs based on optimized sample entropy and extreme learning machine[J].Journal of Neuroscience Methods,2012,210(2):132-146.。
embedding model 指标-概述说明以及解释1.引言1.1 概述概述:概述部分将介绍embedding model以及本文的主要研究内容。
在当今大数据时代,信息爆炸给数据处理和信息检索带来了极大的挑战。
为了更好地处理和利用这些海量数据,embedding model应运而生。
embedding model是一种将高维度数据映射到低维度连续向量空间的方法。
它可以将大规模的离散数据进行编码并进行有效的表示。
通过将每个离散数据映射到低维连续向量空间中的一个向量,embedding model可以保留原始数据之间的关系,并能够更好地捕捉到数据的语义信息。
本文将着重探讨embedding model在实际应用中的指标问题。
指标是衡量embedding model性能的重要标准,它可以用来评估embedding model对于特定任务的效果和表现。
在不同的应用领域中,常用的指标包括准确率、召回率、均方误差等。
本文将结合具体案例和实验结果,分析不同指标的优缺点,帮助读者更好地理解和评估embedding model的性能。
在接下来的章节中,我们将首先介绍embedding model的定义,包括其基本原理和核心概念。
然后,我们将探讨embedding model在各个领域的应用场景,包括自然语言处理、推荐系统、图像处理等。
通过分析不同领域的案例,我们将深入理解embedding model在解决实际问题中的作用和效果。
最后,在结论部分,我们将总结embedding model的优势和发展前景,并展望未来的研究方向。
通过本文的详细探讨,希望能够为读者提供一种全面的了解和评估embedding model的方法,推动其在各个领域的应用进一步发展。
1.2 文章结构文章结构部分的内容可以包括以下内容:文章结构部分旨在介绍整篇文章的组织结构,并说明各个部分的主要内容和目的。
本文分为引言、正文和结论三个部分。
引言部分以概述、文章结构和目的为核心内容。
盘点!深度学习推荐系统中各类流行的Embedding方法(下)作者:Microstrong将门好声音第58期Embedding,中文直译为“嵌入”,也可以被译为“向量化”或者“向量映射”。
形式上来说,Embedding就是用一个低维的向量表示一个物体,可以是一个词,一个商品,或是一个电影。
作为深度学习的“基本核心操作”,Embedding技术已经在深度学习推荐系统中被广泛应用,在Youtube、Airbnb等各类推荐系统中都有涉及。
更多Embedding技术,可以参考往期文章:深度学习推荐系统中各类流行的Embedding方法 (上)。
1. Graph Embedding简介Word2Vec和其衍生出的Item2Vec类模型是Embedding技术的基础性方法,二者都是建立在“序列”样本(比如句子、用户行为序列)的基础上。
在互联网场景下,数据对象之间更多呈现的是图结构,所以Item2Vec在处理大量的网络化数据时往往显得捉襟见肘,在这样的背景下,Graph Embedding成了新的研究方向,并逐渐在深度学习推荐系统领域流行起来。
Graph Embedding也是一种特征表示学习方式,借鉴了Word2Vec的思路。
在Graph中随机游走生成顶点序列,构成训练集,然后采用Skip-gram算法,训练出低维稠密向量来表示顶点。
之后再用学习出的向量解决下游问题,比如分类,或者连接预测问题等。
可以看做是两阶段的学习任务,第一阶段先做无监督训练生成表示向量,第二阶段再做有监督学习,解决下游问题。
总之,Graph Embedding是一种对图结构中的节点进行Embedding编码的方法。
最终生成的节点Embedding向量一般包含图的结构信息及附近节点的局部相似性信息。
不同Graph Embedding方法的原理不尽相同,对于图信息的保留方式也有所区别,下面就介绍几种主流的Graph Embedding方法和它们之间的区别与联系。
第5期李卫等: 基于重建辅助的压缩学习图像分类 115[10]LOHIT S, KULKARNI K, TURAGA P, et al. Reconstruction-Free Inference on Compressive Measurements[C]//2015 IEEEConference on Computer Vision and Pattern Recognition Workshops (CVPRW), June 7-12, 2015, Boston, MA, USA. IEEE, 2015: 16-24.[11]KULKARNI K, TURAGA P. Reconstruction-Free Action Inference from Compressive Imagers[J]. IEEE Transactions onPattern Analysis and Machine Intelligence, 2015, 38(4): 772-784.[12]CALDERBANK R, JAFARPOUR S, SCHAPIRE R. Compressed Learning: Universal Sparse Dimensionality Reductionand Learning in the Measurement Domain[EB/OL]. [2022-09-06]. https:///publication/228364241. [13]张春晓, 鲍云飞, 马中祺, 等. 基于卷积神经网络的光学遥感目标检测研究进展[J]. 航天返回与遥感, 2020, 41(6): 45-55.ZHANG Chunxiao, BAO Yunfei, MA Zhongqi, et al. Research Progress on Optical Remote Sensing Object Detection Based on CNN[J]. Spacecraft Recovery & Remote Sensing, 2020, 41(6): 45-55. (in Chinese)[14]LOHIT S, KULKARNI K, TURAGA P. Direct Inference on Compressive Measurements Using Convolutional NeuralNetworks[C]//IEEE International Conference on Image Processing (ICIP), September 25-28, 2016, Phoenix, AZ, USA.IEEE, 2016: 1913-1917.[15]ADLER A, ELAD M, ZIBULEVSKY M. Compressed Learning: A Deep Neural Network Approach[EB/OL]. [2022-09-06].https:///pdf/1610.09615.pdf.[16]XUAN V N, LOFFELD O. A Deep Learning Framework for Compressed Learning and Signal Reconstruction[C]//5thInternational Workshop on Compressed Sensing Applied to Radar, Multimodal Sensing, and Imaging (CoSeRa), September 10-13, 2018, University of Siegen, Germany. 2018: 1-5.[17]DEGERLI A, ASLAN S, YAMAC M, et al. Compressively Sensed Image Recognition[C]//7th European Workshop onVisual Information Processing (EUVIP), November 26-28, 2018, Tampere, Finland. IEEE, 2018: 1-6.[18]LECUN Y, BOTTOU L, BENGIO Y, et al. Gradient-Based Learning Applied to Document Recognition[J]. Proceedings ofThe IEEE, 1998, 86(11): 2278-2324.[19]KRIZHEVSKY A, NAIR V, HINTON G. The CIFAR-10 Dataset[EB/OL]. [2022-09-06]. /~kriz/cifar.html.[20]GLOROT X, BORDES A, BENGIO Y. Deep Sparse Rectifier Neural Networks[C]//Proceedings of the FourteenthInternational Conference on Artificial Intelligence and Statistics, 2011, 15: 315-323.[21]WEN J, CHEN Z, HAN Y, et al. A Compressive Sensing Image Compression Algorithm Using Quantized DCT and NoiseletInformation[C]//Proceedings of the 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), March 14-19, 2010, Dallas, TX, USA. IEEE, 2010: 1294-1297.[22]PASTUSZCZAK A, SZCZYGIEL B, MIKOLAJCZYK M, et al. Modified Noiselet Transform and Its Application toCompressive Sensing with Optical Single-Pixel Detectors[C]//18th International Conference on Transparent Optical Networks (ICTON), July 10-14, 2016, Trento, Italy. IEEE, 2016: 1-4.[23]ZAGORUYKO S, KOMODAKIS N. Wide Residual Networks[EB/OL]. [2022-09-06]. https:///pdf/1605.07146.pdf.[24]HE K, ZHANG X, REN S, et al. Deep Residual Learning for Image Recognition[C]//2016 IEEE Conference on ComputerVision and Pattern Recognition (CVPR), June 27-30, 2016, Las Vegas, NV, USA. IEEE, 2016: 770-778.[25]HUANG G, LIU Z, MAATEN L V D, et al. Densely Connected Convolutional Networks[C]//2017 IEEE Conference onComputer Vision and Pattern Recognition, July 21-26, 2017, Honolulu, HI, USA. IEEE, 2017: 2261-2269.[26]KRIZHEVSKY A, SUTSKEVER I, HINTON G E. Imagenet Classification with Deep Convolutional Neural Networks[J].Communications of the ACM, 2017, 60(6): 84-90.[27]SIMONYAN K, ZISSERMAN A. Very Deep Convolutional Networks for Large-Scale Image Recognition[EB/OL].[2022-09-06]. https:///pdf/1409.1556.pdf.[28]SHI W, CABALLERO J, HUSZAR F, et al. Real-Time Single Image and Video Super-Resolution Using an EfficientSub-Pixel Convolutional Neural Network[C]//2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 27-30, 2016, Las Vegas, NV, USA. IEEE, 2016: 1874-1883.作者简介李卫,男,1995年生,2018年获河南大学软件工程专业学士学位,现在河南大学电子信息专业攻读硕士学位。
pytorch embedding原理Embedding是将高维稀疏的离散特征转换成低维稠密的特征的一种方法,是深度学习中常用的数据预处理方法之一。
PyTorch中的Embedding模块可以非常方便地实现这个过程。
在自然语言处理中,文本处理成神经网络输入的本质是将字符、词汇等离散嵌入(discrete embedding)到低维向量空间。
Embedding 就是表示 embedding 操作的神经元以及它们之间的链接。
每个神经元对应着原始空间的一个维度 , 神经元之间的链接对应着原始空间中维度之间的联系。
在神经网络中, Embedding 层就被设计成初始化神经元(即初始化一堆浮点数)以及链接的过程,并将文本嵌入到低维向量空间中。
__init__ 函数中我们定义了一个 vocab_size 表示我们的网络中有多少个单词,embed_size 表示可以映射到多少维向量,embedding 这个一个对象,也是我们神经网络的参数,要实现自动梯度计算,需要声明为 Parameter 对象。
首先简单说明一下one-hot向量,假如我们有一个128维的数据集,每个样本都有唯一一个编号,我们可以使用一个128维的one-hot向量来表示每个样本的编号,其中只有一个元素为1,其余为0,例如样本1的编号为42,则该one-hot向量可以表示为[0,0,0,...,0,1,0,0,...,0]。
传统的one-hot向量表示方法的维度非常高,一般在数十万维以上,为了解决这个问题,embedding算法将高维稀疏的one-hot向量映射到低维稠密向量空间中,从而保留原有特征的同时降低数据维度。
Embedding层的输入和输出都是张量,形状为batch_size,seq_length和input_size,其中batch_size表示每个batch的样本数,seq_length表示每个样本的序列长度,input_size表示输入的one-hot向量维度。
微拉美后头套一天带几个小时?看看微拉美恢复过程图微拉美恢复期很痛苦~微拉美恢复过程图:微拉美后头套一天带几个小时?微拉美恢复期很痛苦~【■■■■】做完微拉头套需要佩戴三个月左右,具体时间通常在每天6个小时左右,微拉美后的2**3天会有比较显著的浮肿,要戴上颌颈套来固定,第四天可以摘下颌颈套并外出了,嘴角偶尔会有一些淤青,化妆掩盖就行。
一个周末就可以恢复,然后术后的第10天要拆线。
【■■■■】微拉美的核心在于通过——符合力学设计的埋置,使用可吸收线材形成微创,引导胶原网状生成,通过自身瘢痕网架的形成,支撑面部日益松垂的组织,持续抗衰。
深层需要用比较粗双向螺旋锯齿的线来打地基,激发自体产生新的胶原,激活面部的细胞,如果自身营养不足,在没有配套口服专用营养ACME—TEA细胞激活能量蛋白,可能会导致皮层坏死,就会出现面部凹凸不平的情况,严重点会造成面部塌陷。
The core of micro-Latin America is the embedding of ——conforming to the mechanical design, the use of absorbable wire to form a minimally invasive, guide the formation of collagen mesh, through the formation of its own scar grid, support the increasingly loose facial tissue, and continuous anti-aging. Deep need to use mor e thick two-way serrated line to play foundation, stimulate autologous produce new collagen, activate facial cells, if its nutrition, in the absence of special oral nutrition acme-tea cell activation energy protein, may lead to cortical necrosis, there will be facial uneven, serious point can cause facial collapse【■■■■】(微拉美恢复过程图:微拉美后头套一天带几个小时?微拉美恢复期很痛苦~).lzj↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓微拉美后头套一天带几个小时?看看微拉美恢复过程图微拉美恢复期很痛苦~【●●●●●】线雕提升效果,紧致皮肤,提升组织,解决面部松弛下垂的问题,同时淡化面部细纹,刺激皮下胶原生长,提亮肤色,改善皮肤弹性和光泽等。
uIntegration of Bosch and third party systems through deployment of OPCu All relevant information in one user interface u Fully embedded access controlu Full event log for forensic investigations uScalable system that grows with your needsThe Building Integration System (BIS)BIS is a flexible, scalable security and safetymanagement system that can be configured to handle an enormous spectrum of operational scenarios.It contains a huge range of applications and features which enable both the integration and coupling as well as the monitoring and control of all technical building systems.This new version builds on Bosch's many years of experience in management systems and was considerably influenced by the following market trends:•Increasing complexity of technical building equipment The increasing complexity of technical equipment inside buildings requires a powerful management system which combines the most varied functions (e.g. fire and intrusion alarm systems, access control,video systems and building automation... etc.) in the best possible way. The OPC standard enables BIS to process and share information efficiently with a huge variety of hardware devices and other sources.•Using new technologies and standardsWhile the strict regulations in the field of security technology ensure a high degree of reliability in security matters, they hinder the integrated use of new technologies from the IT world. BIS hassucceeded in harnessing the benefits of non-security-based technologies (e.g. OPC, CAD, web) and harmonizing them with the world of security technologies.•Need for complete solutionsFacility managers and integrators are demanding a single building-management solution that is nevertheless able to integrate all their security subsystems.System overviewThe Building Integration System is a versatile product made up of a basic package plus various optional components (also known as Engines) based on a common software platform. The engines can becombined to tailor building management systems to detailed requirements.These main components are:•Automation Engine •Access Engine •Video Engine •Security Engine* not available in all countriesThese engines are described in greater detail in separate datasheets.FunctionsSystem architectureThe BIS Engines provide fire and intrusion detection,access control, video surveillance plus the monitoring of HVAC and other vital systems.BIS is based on a performance-optimized multi-tier architecture especially designed for use in Intranet and Internet environments.Subsystems are connected via the well-established,world-wide OPC standard. This open standard makes it easy to insert BIS into existing OPC-compliant subsystems.Optionally, individual BIS systems can cooperate by providing data to, or consuming data from, other BISsystems. The result is a Multi-server BIS system.1. A BIS consumer server with workstations and router in a local area network (LAN)2.Wide area network (WAN)3.BIS provider servers with workstations and routers in local area networks (LAN)Organizational structure and configurationA number of automatic functions and easy-to-use tools make configuration installer-friendly, saving time and expense.Hierarchical location trees can be created by theimport of existing CAD data containing layers, named views and detector locations. Zooming and panning allow rapid navigation through the building.The user interface is web -based using dynamic HTML pages. Default pages for different screen resolutions and formats are included in the installation software,and the default pages can easily be customized using a standard HTML editor.BIS automatically detects the monitor resolution and provides the appropriate user interface.OperationThe system’s main task is to operate as the alarm-monitoring and control center for the various security systems within a site. Its graphical interface isdesigned to help the operator grasp the extent and urgency of an occurrence quickly, and to take promptand effective action.The heart of the system, the State Machine, monitors all incoming events and operator requests and, if desired, can take actions prescribed by user-defined rules or Associations, thus unburdening the operators.System securityAES encryption between BIS central server andworkstations provides additional security in addition to configurable user-access rights. If PCs within a corporate network are to be used as clientworkstations then enhanced security can be achieved by restricting operators to specific workstations or IP-addresses.Basic packageThe Building Integration System basic packageprovides many features used in common by the various Engines.•Customizable device condition counters to provide an overview of the condition of subsystems across the entire BIS system•Message processing and alarm display•Alarm queue with up to 5000 simultaneous alarmevents and detailed alarm information•Fixed assignment of operators to workstations for higher security•State machine for automated event and alarm handling.•Web-server-based platform allows client workstations to connect to BIS via just the Internet Explorer •Direct support for location maps in standardAutoCAD DWF vector format reduces configurationeffort.•Changes to architecture within a graphic (new walls,moving a door, etc.) can be implemented without changing the BIS configuration, simply import a new plot file.•Automated workflows between operators, with message broadcasting and customizable escalation paths•Huge library of standardized detector icons in standard vector format including color, event and control definitions•Direct control and monitoring of detectors via the context menus of their icons in the location maps •Direct control and monitoring of detectors via the logical tree-structure (e.g. building – floor – room) of a site, with hyperlinks to photos, manuals,instructions•Location tree generated automatically from the "named views" within the AutoCAD graphic•Action management for automatic and manual control into connected subsystems and their peripherals•Device overview for all connected subsystems, and their peripherals (detectors) and internal virtual devices (operator, server, ...) in the form of a tree structure with detailed information about address,status, type, location and notes. Control theperipherals via the context menus of their tree nodes.•Ability to compartmentalize the managed site into autonomous Divisions, and to restrict operators to the control of specific Divisions.•Ability to provide specific information to the operator in the form of free-form “miscellaneous” hypertext documents, including text, bitmaps, video images,etc.•Highly configurable operator access rights for monitoring and control of subsystems and their peripherals•Event log to ensure all events are completely documented (including messages received and actions taken)•Reporting services to quickly create reports from the event log•Linking and embedding of OPC servers from any computer in the network •Online HelpAction plans and location mapsBIS amplifies standard alarm-handling by its ability to display action plans and location maps, including graphical navigation and the alarm-dependentvisualization of layers inside those maps. This ensures optimal guidance to operators especially in stress situations, such as fire or intrusion alarms.Alarm-dependent action plans or workflows provide detailed event-dependent information such as standard operating procedures, live images, control buttons, etc. to the operator. Simply create and assign one action plan to each possible alarm type in your system, e.g. fire alarm, access denied, technical alarms, etc.With the deletion of an alarm message an unmodifiable snapshot of the displayed action plan is attached to the event log. This ensures accountability by providing a trace of all steps performed by the operator duringthe alarm response.•Location maps are a visualization of premises e.g.floors, areas or rooms, based on the popular AutoCAD vector-graphics format. Detectors and other devicesare represented by colored, animated icons thatprovide direct control via their context menus. In the case of an alarm the system zooms automatically tothe location in the map where it was triggered.• A location tree provides entry points to the locationmap and its graphical navigation functions (pan,zoom).•Alarm-dependent layer control allows the display ofadditional graphical information for specificsituations, e.g. escape routes in case of fire alarms. BIS optional accessoriesThe optional features listed below can be added to the BIS system to meet specific customer requirements. They are usable with all the BIS Engines (Automation, Access, Video and Security Engine).Alarm management packageThis package extends the standard alarm-handling of your BIS system by some additional features: Message distribution allows the definition of escalation scenarios which are activated automatically when an operator or operator group fails to acknowledge an alarm message within a defined period. BIS will then forward the message automatically to the next authorized operator group. The timer feature allows the setup of time schedules which can be used to perform automatic control commands, such as closing a barrier at 8:00 pm, as well as for time-dependent redirection of alarm messages, e.g. within time period 1 show message tooperator group 1 else to operator group 2.The operator alarm feature allows an operator to trigger an alarm manually from the location tree, for example, if informed by telephone of a dangerous situation. Such manual alarms are processed in the same way as those triggered by a detector: that is, the associated documents are displayed and all steps taken are recorded in the event log.The application launcher allows the invocation of non-BIS applications by the system based upon predefined conditions, e.g. alarms or timers. A typical application of this would be for an automatic, scheduled system backup.Building Integration System in figuresParts includedWhen ordered as Installation Media in Box the box contains:ponents1BIS Installation medium with software and installation manuals as PDF1Quick installation guide (printed)When downloaded (Version 4.0 and later) the online documentation is contained in the download.The basic package includes the following licenses: ponents1Operator client license1Division licenseTechnical specificationsMinimum technical requirements for a login or connection serverMinimum technical requirements for a client computerOrdering informationBIS is available in the following languages:•DE = German•EN = English•ES = Spanish•FR = French•HU = Hungarian•NL = Dutch•PL = Polish•PT = Portuguese•RU = Russian•TR = Turkish•ZH-CN = Simplified Chinese•ZH-TW = Traditional ChineseA BIS basic license is required when setting up a new systemBIS 4.1 Basic LicenseLicense for the use of the software as downloadedfrom the website. No physical parts are delivered andthe user documentation is contained in the download.Order number BIS-BGEN-B41BIS 4.1 Installation Media in BoxBox contains the installation medium for all languagesand the Quick Installation Guide.Order number BIS-GEN-B41-BOXBIS 4.1 Alarm Management PackageLicense for the addition to BIS of the feature specifiedOrder number BIS-FGEN-AMPK41BIS 4.1 additional 1 Operator ClientLicense for the addition to BIS of the feature specifiedOrder number BIS-XGEN-1CLI41BIS 4.1 additional 1 DivisionLicense for the addition to BIS of the feature specifiedOrder number BIS-XGEN-1DIV41BIS 4.1 Multi-Server Connect per ServerLicense for the addition to BIS of the feature specifiedOrder number BIS-FGEN-MSRV41BIS Upgrade from 3.0 to 4.xLicense for an upgrade between the versionsspecified.Order number BIS-BUPG-30TO40BIS Upgrade from 2.x to 4.xLicense for an upgrade between the versionsspecified.Order number BIS-BUPG-2XTO40BIS 4.1 BVMS ConnectivityLicense for the connection between one BIS and oneBVMS installationOrder number BIS-FGEN-BVMS41Represented by:Americas:Europe, Middle East, Africa:Asia-Pacific:China:America Latina:Bosch Security Systems, Inc. 130 Perinton Parkway Fairport, New York, 14450, USA Phone: +1 800 289 0096 Fax: +1 585 223 9180***********************.com Bosch Security Systems B.V.P.O. Box 800025617 BA Eindhoven, The NetherlandsPhone: + 31 40 2577 284Fax: +31 40 2577 330******************************Robert Bosch (SEA) Pte Ltd, SecuritySystems11 Bishan Street 21Singapore 573943Phone: +65 6571 2808Fax: +65 6571 2699*****************************Bosch (Shanghai) Security Systems Ltd.203 Building, No. 333 Fuquan RoadNorth IBPChangning District, Shanghai200335 ChinaPhone +86 21 22181111Fax: +86 21 22182398Robert Bosch Ltda Security Systems DivisionVia Anhanguera, Km 98CEP 13065-900Campinas, Sao Paulo, BrazilPhone: +55 19 2103 2860Fax: +55 19 2103 2862*****************************© Bosch Security Systems 2015 | Data subject to change without notice 181****2875|en,V7,30.Nov2015。
Prompt-basedLanguageModels:模版增强语⾔模型⼩结©PaperWeekly 原创 · 作者 | 李泺秋学校 | 浙江⼤学硕⼠⽣研究⽅向 | ⾃然语⾔处理、知识图谱最近注意到 NLP 社区中兴起了⼀阵基于 Prompt(模版)增强模型预测的潮流:从苏剑林⼤佬近期的⼏篇⽂章《必须要 GPT3 吗?不,BERT 的 MLM 模型也能⼩样本学习》,《P-tuning:⾃动构建模版,释放语⾔模型潜能》,到智源社区在 3 ⽉ 20 ⽇举办的《智源悟道1.0 AI 研究成果发布会暨⼤规模预训练模型交流论坛》[1] 中杨植麟⼤佬关于“预训练与微调新范式”的报告,都指出了 Prompt 在少样本学习等场景下对模型效果的巨⼤提升作⽤。
本⽂根据上述资料以及相关论⽂,尝试梳理⼀下 Prompt 这⼀系列⽅法的前世今⽣。
不知道哪⾥来的图……本⽂⽬录:1. 追本溯源:从GPT、MLM到Pattern-Exploiting Training1. Pattern-Exploiting Training2. 解放双⼿:⾃动构建Prompt1. LM Prompt And Query Archive2. AUTOPROMPT3. Better Few-shot Fine-tuning of Language Models3. 异想天开:构建连续Prompt1. P-tuning4. ⼩结追本溯源:从GPT、MLM到Pattern-Exploiting Training要说明 Prompt 是什么,⼀切还要从 OpenAI 推出的 GPT 模型说起。
GPT 是⼀系列⽣成模型,在 2020 年 5 ⽉推出了第三代即 GPT-3。
具有 1750 亿参数的它,可以不经微调(当然,⼏乎没有⼈可以轻易训练它)⽽⽣成各式各样的⽂本,从常规任务(如对话、摘要)到⼀些稀奇古怪的场景(⽣成 UI、SQL 代码?)等等。
Rate-Distortion Optimized EmbeddingJin Li and Shawmin LeiSharp Laboratories of America, Digital Video Division5750 NW Pacific Rim Blvd., Camas, WA 98607, USA.Tel. (360) 817-8486, Fax. (360) 817-8436, Email: lijin@ABSTRACT: In this paper, we improve the perform-ance of the embedded coder by reorganising its output bitstream in the rate-distortion (R-D) sense. In the proposed rate-distortion optimized embedding (RDE), the coding bit is first allocated to the coefficient with the steepest R-D slope, i.e. the biggest distortion de-crease per coding bit. To avoid transmission of the position of the coded coefficient, RDE uses the ex-pectation R-D slope that can be calculated by the coded bits that have already been transmitted to the decoder. RDE also takes advantage of the probability estimation table of the QM-coder so that the calcula-tion of the R-D slope is just a lookup table operation. Extensive experimental results show that RDE signifi-cantly improves the coding efficiency.1. INTRODUCTIONThe embedded image coding receives great attention recently. The representative works of embedding in-clude the embedded zerotree wavelet coding (EZW) proposed by Shapiro [1] , the set partitioning in hier-archical trees (SPIHT) proposed by Said and Pearlman [2] , and the layered zero coding (LZC) proposed by Taubman and Zakhor [3] . In addition to providing a very good rate-distortion (R-D) performance, embed-ded coder has a desirable property that the bitstream can be truncated at any point and still decode reason-able quality image. Such embedding property is ideal for a number of applications such as progressive image transmission, rate control, scalable coding, etc.. EZW and its derivatives achieve embedding by organizing the quantization bit-plane by bit-plane and entropy encoding the significant status or refinement bit. How-ever, there is no guarantee that the rate-distortion performance was optimized at the truncation point.It is well known that the coding achieves optimality if the rate-distortion slopes for all coded coefficients are constant. Xiong and Ramchandran [4] fixed the rate-distortion slope, and applied tree-pruning to spatial frequency quantization to exactly encode each coeffi-cient with the same rate-distortion slope. Although achieving good coding efficiency, the scheme was very complex, and it lost the bitstream embedding property which was very useful in many applications. Li and Kuo [5] showed that the R-D slopes of signifi-cance identification and refinement coding was differ-ent, and by placing the significance identification before refinement coding in each layer, the coding efficiency could be improved. However, the improve-ment of [5] was fairly limited.In this research, we propose a rate-distortion opti-mized embedding (RDE) by allocating the available coding bits first to the coefficient with the steepest R-D slope, i.e. the biggest distortion decrease per coding bit. Considering the synchronization between the en-coder and the decoder, the actual optimization is based on the expectation R-D slope that can be calculated on the decoder side. We take advantage of the probability estimation table of the QM-coder [6] [7] to simplify the calculation of the R-D slope and speed up the algorithm. The algorithm significantly improves the coding efficiency.The paper is organized as follows. The initiative of the rate-distortion optimization is introduced in Sec-tion 2. The framework and the implementation detail of RDE are investigated in Section 3. We focus pri-marily on the two key steps of RDE, i.e., the R-D slope calculation and the coefficient selection. Exten-sive experimental results are shown in Section 4 to compare the performance of RDE with various other algorithms. Concluding remarks are presented in Sec-tion 5.2. CODING OPTIMIZATION BASED ON THE RATE-DISTORTION SLOPE For convenience, let us assume that the image has already been converted into the transform domain. The transform used in embedded coding is usually wavelet decomposition, but it can be DCT as well, as in [10] . Let the index position of the image be denoted as i=(x,y), let the coefficient at index position i be de-noted as w i. Suppose the coefficients have been nor-malized with absolute maximum value of 1. Because w i is between –1 and +1, it can be represented by a binary bit stream as:±0.b1b2b3...b j (1)where b j is the jth most significant bit (MSB) of coef-ficient w i. Traditional coding first determines the bit-depth n (or quantization precision), then sequentially encodes one coefficient by another. For each coeffi-cient w i, the most significant n bits are bound together with the sign±0.b1b2b3…b n(2) and encoded by the entropy coder. The quantization precision is predetermined before coding. If the coding bitstream is truncated, the bottom half of the coeffi-cients will be lost. Embedded coding is distinctive from traditional coding in the sense that the image is coded bit-plane by bit-plane rather than coefficient bycoefficient. It first encodes bit b1 of coefficient w1, then bit b1 of w2, then bit b1 of w3, etc.. After the bit plane b1 of all coefficients has been encoded, it moves on to bit plane b2, and then bit plane b3. In the em-bedded coding, each bit is an independent coding unit. Whenever a coefficient w i becomes nonzero, its sign is encoded right after. The embedded coding bitstream can be truncated at any point with graceful quality degradation since at least part of each coefficient has been coded.Although the bit-plane oriented embedded coding is better than the coefficient oriented coding, it is still not optimal in the rate-distortion (R-D) sense. We illus-trate the initiative in Figure 1. Suppose there are five symbols a, b, c, d and e that can be coded independ-ently. Coding each symbol requires a certain amount of bits and results in a certain amount of coding dis-tortion decrease. Coding of all symbols sequentially gives an R-D curve shown as the solid line in Figure 1. If the coding order is reorganized so that the symbol with the steepest R-D slope is encoded first, we can get an R-D curve shown as the dashed line in Figure 1. Though both lines reach the same final R-D point, the algorithm that follows the dashed line performs better when the coding is truncated at an intermediate bit rate. Therefore, the initiative of the rate-distortion optimized embedding (RDE) is to allocate the avail-able coding bits first to the coefficient with the steep-est R-D slope, i.e., the coefficient with the biggest distortion decrease per coding bit. Note when all bits have been coded (i.e., the coding achieves lossless), RDE will have exactly the same performance as its counterpart without R-D optimization. However, in a practical wide bit rate range, RDE will outperforms traditional embedding significantly.3. IMPLEMENTATION OF RATE-DISTORTION OPTIMIZED EMBED-DING (RDE)The framework of the RDE can be shown in Figure 2. In general, RDE calculates the R-D slope, or the dis-tortion decrease divided by the coding bits, for the candidate bit of all coefficients. It then encodes the coefficient w i that has the steepest R-D slope, i.e., the biggest distortion decrease per coding bit. Such coding strategy achieves embedding with optimal R-D per-formance. If the coding bit stream is truncated, the performance of coding at that bit rate will be optimal. Since the actual R-D slope will not be available at the decoder, RDE uses the expectation R-D slope that can be calculated by the already coded bits. By doing so, the decoder can derive the same R-D slope and track the coefficient to be transmitted next just the same as the encoder. Therefore, the location information of w i does not need to be transmitted.3.1 Calculation of Rate-Distortion SlopeThe two key steps of RDE are coefficient selection and R-D slope calculation. In this subsection, we de-velop a very efficient algorithm which calculate the R-D slope with just a lookup table operation.For coefficient w i, assume the most significant n i-1 bits have already been coded, and the n i th bit is the next bit to be processed. We call n i as the current coding layer, and the n i th bit of w i as the candidate bit. The situation is shown in Figure 3, where the coded bits are marked with slashes, and the candidate bits are marked with horizontal or vertical bars. As traditional embedded coding, RDE classifies the coding of candi-date bits into two categories – significance identifica-tion and refinement coding. For coefficient w i, if all previous coded bits b j are ‘0’ for j=1...n i-1, the sig-nificance identification mode is used for the n i th bit. If either one of the previous coded bits is ‘1’, the refine-ment mode is used. We show an example in Figure 3, where the bits undergone significance identification are marked by vertical bars, and the bits undergone refinement coding are marked by horizontal bars. The R-D slopes for the two modes are very different.The significance identification mode classifies coeffi-cient w i from interval (-2T,2T) to interval (-2T,-T] of negative significance, (-T,T) of non-significance, and [T,2T) of positive significance, where T=2-n i is the width of the coding interval determined directly by the current coding layer n i. From the coding interval, we can easily derive the decoding reconstruction before significance identification as:r b=0 (3) and the decoding reconstruction for negative signifi-cance, non-significance, positive significance as:r s-,a=1.5T, r i,a=0 , r s-,a=1.5T(4) respectively. In significance identification, the coded symbol is highly biased towards non-significance. We encode the result of significance identification with a QM-coder, which estimates the probability of signifi-cance p i with a state machine, and then arithmetic encodes the result. As shown in Figure 4, the QM-coder uses a context which is a 7-bit string with each bit representing the significant status of one spatial neighbor coefficient or one coefficient at the same spatial position but in the parent band of current coef-ficient w i. By monitoring the pattern of past 0s (‘insig-nificance’) and 1s (‘significance’) under the same context (i.e., the same neighborhood configuration), the QM-coder estimates the probability of significance p i of the current coding symbol. The probability esti-mation is very simple for QM-coder, as it is just a state table transition operation. For details of the QM-coder and its probability estimation, we refer to [6] [7] . Assuming the QM-coder performs closely to the Shannon bound for coding the result of significance identification, we may calculate the expectation coding rate as:E[D R]=(1-p i ) D R insig +p i D R sig=(1-p i ) [-log 2(1-p i )]+p i (-log 2p i +1) =p i +H(p i )(5)where H(p i ) is the entropy of a binary symbol with probability of 1 equals to p i . Note that in (5), when the symbol becomes significant, it needs one additional bit to encode the sign of significance. With the known probability of significance p i , the expectation distor-tion decrease of significance identification can be calculated as:E[D D] =(1-p i ) D D insig +p i D D sig (6)where D D sig and D D insig can be further calculated by taking the probability weighted average of the coding distortion decrease:D D insig =õó-T T[(x-r b )2-(x-r i,a )2]p(x)dx (7)D D sig =õó-2T -T[(x-r b )2-(x-r s-,a )2]p(x)dx+õóT2T[(x-r b )2-(x-r s+,a )2]p(x)dx (8)By substituting (3) and (4) into (7), it becomes:D D insig =0 (9)There is no coding distortion decrease if w i is still insignificant. To calculate D D sig , we need the a priori probability distribution of coefficient w i within the significance interval (-2T,-T] and [T,2T). Note that the probability distribution of w i within interval (-T,T) is irrelevant to the calculation of distortion decrease.Assuming that the a priori probability distribution within the significance interval is uniform, we can derive:p(x)=12T, for T<|x|<2T (10)Based on (3), (4), (8) and (10), we conclude thatD D sig =2.25T 2 (11)The expectation distortion decrease for significance identification is therefore:E[D D]=p i 2.25T 2(12)It is straightforward to derive the R-D slope of signifi-cant identification w i as:l sig =E[D D]E[D R]= 2.25T 21+H(p i )/p i(13)Functionf s (p i )=11+H(p i )/p i(14)is plotted in Figure 5. It is apparent that the symbol with higher probability of significance has a larger rate-distortion slope and is thus favored to be encoded first.We may similarly calculate the R-D slope of refine-ment coding mode. The refinement coding classifies coefficient w i from interval [S,S+2T) to interval[S,S+T) or [S+T,S+2T), where T=2-n i is again deter-mined by the coding layer n i , and S is the start of the refinement interval, which is the value indicated by the coded bits of the coefficients. The decoding recon-struction before refinement coding is:r b =S+T (15)Depending on the coding result, the decoding recon-struction after refinement becomes:r 0,a =S+0.5T, r 1,a =S+1.5T (16)Because the refinement coding is equilibrium between ‘0’ and ‘1’, the expectation coding rate is close to one bit.E[D R]=1.0 (17)Similar to (6), the expectation distortion decrease can be calculated as:E[D D] =õóS S+T[(x-r b )2-(x-r 0,a )2]p(x)dx+õóS+TS+2T[(x-r b )2-(x-r 1,a )2]p(x)dx (18)Assuming that the a priori probability distribution with in interval [S,S+2T) is uniform, i.e., p(x)=1/2T,we conclude for refinement coding:E[D D] =0.25 T 2(19)The R-D slope of refinement coding is thus:l ref =E[D D]E[D R]=0.25T 2 (20)Compare (13) and (20), it is apparent that for the same coding layer n i , the R-D slope of refinement coding is smaller than that of significance identification when-ever the significance probability p i is above 0.01. Thus in one coding layer, significance identification should be in general placed before the refinement coding, as indicated in [5] .We have also modeled the a priori probability func-tion of coefficient w i to be Laplacian. In such case, the R-D slope for significance identification and refine-ment coding becomes:l sig = 2.25T 21+H(p i )/p i g sig (s ,T)(21)l ref = 0.25T 2 g ref (s ,T) (22)where s is the variance of Laplacian distribution which is again estimated from the already coded bits,and g sig (s ,T) and g ref (s ,T) are Laplacian modifica-tion factors in the form of:g sig (s ,T)=12.25èçæø÷ö0.75 + 3s T - 3e -T/s 1-e -T/s (23)g ref (s ,T)=4èççæø÷÷ö0.75 + 2s Te -T/s - s T ()1+e -2T/s 1-e -2T/s (24)However, experiments show that the additional per-formance improvement provided by the Laplacianmodel is minor. Since the uniform probability distri-bution model is much simpler to implement, it is used throughout the experiment.Because the probability of significance p i determined by the QM-coder state is discrete, and the width of interval T determined by the coding layer n i is dis-crete, both R-D slope (13) and (20) have a discrete number of states. For fast calculation, (13) and (20) may be pre-computed and stored in a table indexed by the coding layer n i and the probability state of QM-coder. Thus, computation of the R-D slope will be only a lookup table operation. The number of entries M of the lookup table can be calculated by:M=2xNxL+N(25) where N is the maximum coding layer, L is the num-ber of states in the QM-coder. In the current imple-mentation of RDE, there are a total of 113 states in the QM-coder, and a maximum of 20 coding layers. This brings a lookup table of size 4540.3.2 Coefficient Selection and Flowchart of Rate-Distortion OptimizationThe second key step in RDE is selecting the coeffi-cient with the maximum R-D slope. Since an exhaus-tive search or a sorting over all image coefficients is computational expensive, a threshold based selection approach is introduced in this subsection. We first set an R-D slope threshold l. The whole image is scanned and those coefficients with R-D slope greater than l are encoded. The R-D slope threshold l is then re-duced by a certain factor and the whole image is scanned again.The coding operation of RDE can be shown in Figure 6. It can be described step by step as:1)The image is decomposed by the wavelettransform.2)The initial R-D slope threshold l is set to l0, with:l0 =0.25x0.52=0.03125(26) 3)The image is scanned and coded.The scan goes from the coarse scale to the fine scale, and follows the raster line order within the subband.4)For each coefficient, its expectation R-D slope iscalculated.Depending on whether the coefficient is already significant, the R-D slope is calculated by (13) and (20), respectively. Note that the calculation of the R-D slope is only a lookup table operation indexed by the QM-coder state and the coding layer n i.5)The calculated R-D slope is compared with l.If the R-D slope is smaller than l, the coding proceeds to the next coefficient. Only those coefficients with R-D slope greater than l are encoded.6)The coefficient is encoded with significantidentification or refinement coding.The bit of significance identification is encoded by a QM-coder with context designated in Figure 4. The bit of sign and the bit of refinement are encoded by a QM-coder with fixed probability 0.5.7)The coder checks if the assigned coding rate isreached. If not, it repeats step 4) until the entire image has been scanned.8)The R-D slope threshold is reduced by a factor ofa:l¬l/a(27) In our current implementation, a is set to 1.25. The coder then goes back to step 3) and scans the entire image again.4. EXPERIMENT RESULTSExtensive experiments are performed to compare RDE with two existing algorithms. One is a predictive embedded zerotree wavelet (PEZW) coding which is an improved version of the original EZW and is cur-rently in the MPEG4 verification mode (VM) 6.0. We use PEZW as a reference for the state-of-the-art wavelet coding technique. The other one is the layered zero coding (LZC) proposed by Taubman and Zakhor. RDE encodes the bit of significance identification and the bit of refinement very similar to the one used by the LZC. In essence, RDE shuffles the embedded bitstream of LZC to improve its performance. We therefore compare the RDE with LZC to show the advantage of rate-distortion optimization. Two ex-perimental images are used. One is the famous Lena of size 512x512, the other one is the first frame of Akiyo, which is a MPEG4 test image of size 176x144 (QCIF) or size 352x288 (CIF). The Lena image is decom-posed by a 5-level 9-7 tap biorthogonal Daubechies filter [8] as in most of the other coding literature. The Akiyo image is decomposed according to the specifi-cation in MPEG4 VM 6.0 with a 9-3 tap biorthogonal Daubechies filter [8] of 4-levels for QCIF and 5-levels for CIF.The performance of RDE versus LZC of Lena for bit rate range 0.15bpp to 1.0bpp is shown in Figure 7. We plot the R-D performance curve of LZC with dashed line, and plot the R-D performance curve of RDE with solid line. For the clarity of the result, we split the result into 3 subgraphs with bitrate range 0.15-0.30bpp, 0.40-0.60bpp and 0.70-1.00bpp. RDE out-performs LZC by 0.2-0.4dB over the entire bit rate range. The performance advantage becomes larger at higher bitrate. The R-D performance curve of RDE is also much smoother than that of LZC. In Table 1, we show the performance comparison of PEZW, LZC and RDE on Akiyo image at 10k, 20k and 30k bits for QCIF and 25k, 50k and 70kbits for CIF. The result of PEZW is obtained from document [9] . It is shown that the performance gap between LZC and RDE becomes larger for a low-detailed image as Akiyo. In general, RDE outperforms LZC for 0.4-0.8dB, and outperforms PEZW for 0.3-1.2dB for Akiyo image over a variety of bitrate.5. CONCLUSIONSIn this paper, we propose a rate-distortion optimized embedding (RDE) algorithm. By reordering the em-bedding bitstream so that the available coding bit is first allocated to the coefficient with the steepest R-D slope, i.e. the biggest distortion decrease per coding bit, RDE substantially improves the performance of embedded coding. For synchronisation between the encoder and the decoder, RDE uses the expectation R-D slope which can be calculated at the decoder side with the already coded bits. RDE also takes advantage of the probability estimation table of the QM-coder so that the calculation of the R-D slope is just one lookup table operation. Extensive experimental results con-firm that RDE significantly improves the coding effi-ciency.6. REFERENCES[1] J. Shapiro, “Embedded image coding using zero-tree of wavelet coefficients”, IEEE Trans. On Signal Processing, vol. 41, pp.3445-3462, Dec. 1993.[2] A. Said, and W. Pearlman, “A new, fast and effi-cient image codec based on set partitioning in hierar-chical trees”, IEEE Trans. On Circuit and System for Video Technology, Vol. 6, No. 3, Jun. 1996, pp. 243-250[3] D. Taubman and A. Zakhor, “Multirate 3-D sub-band coding of video”, IEEE Trans. On Image Proc-essing, Vol. 3, No. 5, Sept. 1994, pp.572-588.[4] Z. Xiong and K. Ramchandran, “Wavelet packet-based image coding using joint space-frequency quan-tization”, First IEEE International Conference on Image Processing, Austin, Texas, Nov. 13-16, 1994. [5] J. Li, P. Cheng and C. -C. J. Kuo, “On the im-provements of embedded zerotree wavelet (EZW) coding”, SPIE: Visual Communication and Image Processing, vol. 2601, Taipei, Taiwan, May. 1995, pp. 1490-1501.[6] W. Pennebaker and J. Mitchell, IBM, “Probability adaptation for arithmetic coders”, US patent 5,099,440, Mar. 24, 1992.[7] D. Duttweiler and C. Chamzas, “Probability esti-mation in arithmetic and adaptive Huffman entropy coders”, IEEE Trans. On Image Processing, vol. 4 no. 3, Mar. 1995, pp. 237-246.[8] M. Antonini, M. Barlaud, P. Mathieu, and I. Dau-bechies, “Image coding using wavelet transform,”IEEE Trans. on Image Processing, Vol. 1, pp. 205-230, Apr. 1992.[9] J. Liang, “Results Report on Core Experiment T1: Wavelet Coding of I Pictures,” ISO/IEC JTC1/SC29/WG11 MPEG97/M1796,Feb.1997. [10] J. Li, J. Li, C.-C. Jay Kuo, “Layered DCT still image compression”, IEEE Trans. On Circuit and System for Video Technology, Vol. 7, No. 2, pp.440-443, Apr. 1997.DRabcd(D0,R0)cadbee(D end,R end)Figure 1 Initiative of rate-distortion optimization.B eginE valuate the R-Dslope of all sym bolSelect the coeff. w ithm axim um R-D slopeE ncode this coeff.R ate reached?E ndYNFigure 2 The framework of rate-distortion optimized embedding.0+-+Sign b1 b2 b3 b4 b5 b6 b7101101100101000001010001110.....................0110001. . . .. . . .. . . .. . . .. . . ....+-w1w2w3w4...w nFigure 3 Element of rate-distortion optimized embed-ded. (The already coded bits are marked with slashes, the candidate bits of significance identification with vertical bars, the candidate bits of refinement coding with horizontal bars. )Figure 4 Context for QM-coder. ( is the current coding coefficient w i , are its context coefficients. )0.20.40.60.810.10.20.30.40.50.60.70.80.91pS i g f a c tFigure 5 The rate-distortion slope modification factor for significance identification.Begin l ¬l 0Scanning: all coefficients Rate reached?EndEncode coefficient with R-D slope greater than ll l /amode?Cal R-D slope for sig. id.Cal R-D slope for refinementR-D slope > l ?NY sigrefNmode?significance identificationsigrefinement codingref Y Figure 6 The flowchart of rate-distortion optimized embedding.0.160.180.20.220.240.260.2831.53232.53333.53434.535Rate(bpp)P S N R (d B )( a )0.40.450.50.5535.53636.53737.538Rate(bpp)P S N R (d B )( b )0.70.750.80.850.90.9513838.53939.54040.5Rate(bpp)P S N R (d B )( c )Figure 7 Comparison between RDE (solid line) and LZC (dashed line) for Lena image with bitrate range (a) 0.15-0.3bpp, (b) 0.4-0.6bpp, (c) 0.7-1.0bpp.Table 1 Experimental result for image Akiyo.LZCPEZWRDESize Bit Rate (bits)PSNR_YPSNR_UPSNR_V (dB)Bit Rate (bits)PSNR_Y PSNR_UPSNR_V (dB)Bit Rate (bits)PSNR_Y PSNR_UPSNR_V (dB)QCIF 1000032.3834.6737.1210256 32.334.236.91000033.1335.0237.90QCIF 2000037.3039.1841.1820816 37.539.141.02000037.9740.0342.17QCIF 3000041.4043.5644.0029240 40.841.542.63000042.0144.2344.75CIF 2500034.6938.2540.3825112 34.737.740.12500035.0338.2341.03CIF 5000039.2341.7244.2449016 39.341.343.65000040.0442.4644.73CIF 7000042.3544.5846.1270448 42.243.245.27000043.0344.3546.39。