Lossless Compression of DSA Image Sequence Based on PCMD2 CoderJi Zhen, Mou Xuanqin, Jiang Yifeng, Cai YuanlongImage Processing Center, Xi’an Jiaotong Univ.Xi’an, P.R.C., 710049E-mail:**************.cn,**************.cnABSTRACT:ⅠINTRODUCTIONMedical image compression has been mainly concerned with lossless coding techniques[1], which ensure that all significant information for diagnostic purposes is retained in the reconstructed images with the compression ratio of around 2:1.The Digital Image and Communications in Medicine proposed standard (DICOM3),that adopted by the American College of Radiology and National Electrical Manufacturing Associa-tion(ACR-NEMA), includes lossless coding and compression of medical images. However, recent studies concerning “Visually lossless” and “In-formation preserving” indicate that the reconstruc-tion error is accepted from a medical point of view. ACR-NEMA announced a call for proposals for lossy compression that has been included in DI-COM3.0 in 1995. This class of compression tech-niques is subjective definitions and extreme cau-tion msut be taken into considerance in P.R.C,where the criteria remains ambiguous and many complex legal and regulatory issues would arise.The objective of compressing images is to reduce the data volume and achieve a low bit rate. Compressing a digital medical image can facilitate its storage and transmission. With regard to the legislation problems, physician prefers diagnosing with uncorrupted medical image. The popular lossless coding schemes includes Huffman, arith-metic, run-length encoding(RLE) and LZW[2]. More effective coding method is desired for the fast growth of PACS (Picture Archiving and Communication System) and Teleradiology.Acqusition of 3-D and 4-D medical image sequences are becoming more usual nowadays, especially in the case of dynamic studies with MRI,CT,DSA,PET. A new lossless compression method is proposed for the image sequence gener-ated by DSA ( Digital Subtraction Angiography ) apparatus, which is now common as X-ray, CT. Compressing an image sequence is equal to com-pression of 3D data, which contains both space and time redundance. The well-known MPEG[3] provides the perfect resolution of the lossy codingof image sequence. It has proved effective and proposed many practicable techniques, which could be exploited.Differential pulse code modulation (DPCM)[4] predictive coding method is predomi-nant in lossless compression. In this paper, high order(2-order) DPCM coder is introduced that can exploit the correlation between one-order differen-tial images and two-order ones to benefits of com-pression, which has highly competitive compres-sion performance and remains practical. We pre-sent the description of this proposed lossless image sequence coder in followed sections.ⅡCHARACTERISTICS OF DSA IMAGESImage compression techniques usually consistof concrete mathematical models. In practical ap-plications, the specific images, for which the available priori knowledge could be exploited in order to develop an optimized compression scheme.A typical DSA image sequence is shown in Figure 1,which consists of :Figure 1. a typical DSA image sequence (a) M represents mask image, acquired before in-travenous or intraarterious injection. (b) L(n) means the sequence of live images, acquired after intravenous or intraarterious injection. N is the volume of the whole sequence. (c) S(n) is the sub-traction image. S(n)=L(n)-M (n=0,…,N-1).(d) SD(n) is the differential subtraction image. SD(n)=S(n)-S(n-1) (n=1,…,N-1). It is obvious that the whole sequence could be repre-sented in three equivalent formats: Format 1. M and L(n); Format 2. M and S(n);Format 3. M 、S(0) and SD(n).Firstly, the entropy of whole images is calcu-lated separately, H x pp jj j()log ,=−∑ (p jmeans the probability of the jth gray in a image). The followed table could be acquired. In this table. The image resolution is 1024*1024*10bits. Table 1Image H(x) M 6.65 L(n) 6.61 S(n) 4.68 SD(n) 3.67Secondly, the correlation between two images is defined as {})()()(k n I n I E k R +⋅=. We separately obtain the correlation of S(n) and SD(n). The correlation between S(n) is shown in Figure 2(a) and between SD(n) is in (b).From the above curve, followed conclusions about the characteristic of DSA images could be made:(a) when K<5, the correlation R(k) between S(n) often remains very high.(b) the correlation R(k) in SD(n) decreases quickly while K increases. However, the R(1) could hold 0.60, which is useful and important in the pro-posed compression method.Since the three represent formats are equivalent in the mathematical mean, compressing the whole sequence could be implemented in three ways, which would take use of different tech-niques and get different results. It is evident that compression result would better by adopting the last represent than two others because of followed reasons: 1.the entropy is smallest, which mean that the highest lossless compression ratio is prospec-tive theoretically. 2.the R(k) of common signal decreases distinctly after applying one-order dif-ferential, Which means that the two-order differ-ential operation seems worthless. However, it is not the same for the DSA images. The correlation between S(n) holds high, which results in the cer-tain meanness of two-order differential images SD(n). The compression performance would be improved by taking the full advantage of this characteristic.Ⅲ COMPRESSION FRAMEWORK A. Differential Pulse Code ModulationDifferential pulse code modulation(DPCM) exploits the property that the values of adjacent pixels in an image are often similar and highly correlated. The general block diagram of DPCM is shown in Figure 3.The value of a pixel is predictedas a linear combination of a few neighbor pixel values, which is represented as follows: ∑∈−−=Rj i r e n j m i X n m X ),(),(),(αwhere e X is the predicted value, R meansa. R(k) between S(n)b. R(k) between SD(n)Figure 2. the R(k) curve of S(n) and SD(n)xEncoderDecoderneighbor region, ),(n m αare prediction coeffi-cients specified by the image characteristic. Theprediction error defined as ),(),(),(j i X j i X j i e e−= is then coded and trans-mitted. The Decoder reconstructs the pixels as ),(),(j i e j i X X q e r +=In order to keep lossless compression, only thepredictor would be included in DPCM coder. It isa “Predictor + Entropy Coder” lossless DPCMcoding .[5]B. Two Order Differential Pulse Code ModulationThe D PCM 2 coder is different from thetwo-demensional(2-D)DPCM method andthree-demensional(3-D) one[6].For a pixel ),,(j i n X in S(n), applying the DPCM withthe variable n indicates the its extension ofthree-dimension. The same is for the SD(n,x,y) in Format 3, which means two order differential be-cause SD(n) is derived from one differential op-eration oneself. The D PCM 2 coder includes four steps:1.For the mask image M, apply the RICE[7]coding method.2.Construct an optimal predictor. The ARMR model is adopted according to the image attribute. The equation is : )()1,1()1,1(),1()0,1()1,()1,0(e r X X b n m Xr n m Xr n m Xr X −+−−+−+−=αααThe last component of right part means the two-order differential and there is not quantization er-rors.3.For the every pixel S(n,x,y) in S(n), apply to the linear prediction with the variable n.4.Apply adaptive arithmetic algorithm to the error signal ),,(y x n e p . The whole coding process is shown in Figure4.Figure 4. the scheme of D PCM 2coding The dash rectangle constitute the D PCM 2 lossless coder. The decoding process is obvious . Ⅳ EXPERIMENTAL STUDY Figure 5 shows typical DSA images acquiredin Forth Military Medical Univ. of P.R.C. The fig-ure gives the image M, L(60),S(60),S(59) and SD(60) separately. The compression results through this pro-posed method are given as follows: average image size after compression is 463Kbyte. average compression ratio cr ==102410241046364782261***.:average bit rate pixel bit B /42.41024*10248*579338== average compression efficiency η===H x B ()..44236783% The followed table gives the compari-son with Huffman,Arithmetic and DPCM. The compression procedure is equivalent to still image compression without reducing the correlation between images.Huffman Arithmetic DPCM D PCM2Cr 1.36:1 1.47:1 1.53:1 2.26:1 B7.35 6.76 6.76 4.42From above table, it is obvious that this proposed compression technique performs better than others.ⅤCONCLUSIONWith applying the proposed method to the DSA apparatus, perfect experiment performance is deserved. The compression ratio is better than or-dinary techniques. The computational time and space also prove practicable and robust. Although significant progress Many researches remain.ACKNOWLEDGMENTThe authors wish to thank Dr.Sun Li-jun,FMMU for his cooperation on acquisition of some important DSA images.(a) M (b) L(60)(c) S(60) (d) S(59) (e) SD(60)(enhancement for display)Figure 5. (a) mask image (b) live image (c)and (d) subtraction image (e) differential subtraction image1.S.Wong, L.Zaremba.D.Gooden,and H.K.Huang. “Radiologic image compression-A Reivew”,Proc. IEEE,vol,83,pp194-219,Feb.1995.2.A.K.Jain, Fundamentals of Digital Image Processing. 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