Volumetric medical data (CT,MR) are useful tools for diagnostic investigation however their usage may be made diffcult because of the amount of data to store or because of the duration of communication over a limited capacity channel. In order to code such information sources we present a progressive three dimensional image compression algorithm based on zerotree wavelet coder with arithmetic coding. We make use of a 3D separable biorthogonal wavelet transform and we extend the zerotree SPIHT algorithm to three dimensions. Moreover we propose some improvements to the SPIHT encoder in order to obtain a better rate distortion performance without increasing the computational complexity. Finally we propose an efficient context-based adaptive arithmetic coding which eliminates high order redundancy. The results obtained on progressive coding of a test CT volume are better than those presented in recent similar works both for the mean PSNR on the whole volume and for the PSNR homogeneity between various slices

A. SIGNORONI

ARRIGONI M

LAZZARONI F

LEONARDI R

SIGNORONI, Alberto

LEONARDI, Riccardo

Archivio istituzionale della ricerca - Università di Brescia

IMPROVING SPIHT BASED COMPRESSION OFVOLUMETRIC MEDICAL DATAA  Signoroni M  Arrigoni F  Lazzaroni R  LeonardiSignals and Communications Lab   DEA  University of Brescia Italyvia Branze   I Brescia Italy Tel 	  Fax 	 e mail fsignoronleongingunibsitABSTRACTVolumetric medical data CT MR are useful toolsfor diagnostic investigation however their usagemay be made dicult because of the amount ofdata to store or because of the duration of communication over a limited capacity channel  In order to code such information sources we presenta progressive threedimensional image compressionalgorithm based on zerotree wavelet coder witharithmetic coding  We make use of a D separable biorthogonal wavelet transform and we extend the zerotree SPIHT algorithm to three dimensions  Moreover we propose some improvementsto the SPIHT encoder in order to obtain a betterratedistortion performance without increasing thecomputational complexity  Finally we propose anecient contextbased adaptive arithmetic codingwhich eliminates high order redundancy  The results obtained on progressive coding of a test CTvolume are better than those presented in recentsimilar works both for the mean PSNR on the wholevolume and for the PSNR homogeneity betweenvarious slices   INTRODUCTIONToday the need to store and communicate largeamounts of biomedical image data requires thestudy of new compression techniques  There existsa rich literature and standardization work e g  theupcoming JPEG regarding twodimensionalimage coding  Diagnostic imaging techniques forexample computed tomography CT or magneticresonance MR produce a stack of D slices making up a D volume  Obviously compression of suchvolume can be accomplished separately for eachslice with a traditional D image coder  Howeverthis does not exploit the strong correlation thatmay exist between adjacent slices  Such correlationis inuenced by the selected resolution along thescanning axis   If the distance between slicesin the z direction is of the same order of magnitudewith respect to the xy resolution i e  the voxelanisotropy is low D coding is performing muchbetter than repeated D one or with respect tovideo coding due to the lack of classical movementin a D scansion  and   The computational coding cost is a critical factor especially formultidimensional data  Nowadays among the bestD compression schemes wavelet based zerotreecoding oers high ratedistortion performance withlow algorithmic complexities  Moreover zerotreeschemes may produce progressive bitstream andallow an easy extension to Region of Interest coding these aspects are essential for biomedical applications In this work we develop a D extension ofthis type of coders  We use a D separable wavelettransform which makes use of the 	 spline lters of  and the more recent  tap ltersproposed in   These lters have demonstratedvery good performance according to objective aswell as perceptual criterion for natural images  Forthe quantization strategy we use the SPIHT algorithm  in order to obtain a bitplane progressivecoding  Beyond extending the SPIHT methodology to D we have modied it slightly introducingan improvement in its ratedistortion performancethrough the elimination of redundant bits and moreadvantageous coecient reconstruction procedure The output of the SPIHT algorithm is coded in order to eliminate the remaining statistical redundancy  For this purpose we develop a contextmodeling scheme for D SPIHT based on algorithmic features of the SPIHT and the statistic correlation between various coecients of the wavelettransform  Finally we test our coding scheme andcompare the results to those obtained on a standardvolume by two recent similar works   D IMPROVED SPIHT   D SPIHT referencesWe rst refer to the D SPIHT approach as presented in   SPIHT is a progressive algorithmcomposed of two iterative steps a signicance mapcoding and a renement pass  The rst step identies signicant coecients i e  larger than a giventhreshold which is a power of two and codes theirposition  The second step renes the signicantlymarked coecients to reduce the uncertainty interval of these coecient values  For coding thesignicance map eciently the wavelet coecientsare reorganized in a collection of spatial orientationtrees  In fact in the case of natural data we canexpect a statistical drop of the wavelet coecientsamplitude from roots towards leaves from low tohigh resolution  The following sets are used to locate the signicant coecients  Di  j set of all descendants of node i  j  Oi  j set of all ospring of node i  j  Li  j Di  jOi  j    D extension of SPIHTThe extension of the SPIHT algorithm to three dimensions is very easy  In fact it is sucient to modify the collection of spatial orientation trees by considering also the third dimension  In this way thenodes now have eight sons instead of four  Moreover the wavelet subbands are numbered in such away to favor for a same decomposition level thoseones highpassltered in the z direction because weexpect to have higher coecients in these subbandsa cause of the voxel anisotropy   Optimization of SPIHT algorithmBeyond extending the SPIHT methodology to threedimensions we make two changes in the basicalgorithm obtaining an improvement in its ratedistortion performance without increasing its computational complexity  First we improve the coding of the signicance map by removing some redundant bits  In fact with reference to the algorithm exposed in  there are three situationswhere the following bit in the encoded stream iscertainly equal to one i e  the set is signicant  when the set D is signicant and all the sonsare insignicant then the set L is signicant  when D is signicant L is empty we are atthe leaves of tree and the rst three seven inD sons are insignicant then the last son issignicant  nally when L is signicant and its rst threeseven in D subsets D are insignicant thenthe last set D is certainly signicant Removing these redundant bits from the encoding of the signicance map we obviously obtain abetter compression ratio The second improvement concerns the coecientreconstruction procedure of the decoder  For eachposition in the bit stream the reconstructed valueof each coecient is the middle of its uncertaintyinterval  In the original SPIHT algorithm this valueis roundedup to the nearest integer  But considering the subband coecient statistics we can reasonably assume the histograms to be monomodalwith a peach in zero and a monotonically decreasing behavior towards higher value  Thus the pdfof the quantization error in each bitplane intervalis slanted towards negative error values  For thisreason it is more convenient to round to lower integer  In this way the original bit stream remainsthe same but the mean square error of the reconstructed image is reduced  Thanks to these twochanges we obtain an increment of the PSNR ofabout    dB both for D images and for medical CT or MR volumes at rate values from   to  bit per pixel as an example we show in Fig the PSNR increment measured by coding the testvolume CT SKULL xx voxels 0.5 0.6 0.7 0.8424344454647Rate (bit per pixel)PSNR (dB)Modified 3D SPIHT Original 3D SPIHT Figure   Comparative evaluation of original andimproved DSPIHT  CONTEXTMODELING IN ARITHMETIC CODINGTo increase the coding eciency the SPIHT bitstream is entropy coded using a contextbasedadaptive arithmetic coder   For identifying themost useful contexts we analyze here the SPIHT algorithm as a binary memory symbol source  Firstwe can identify three main contexts in the structureof the SPIHT algorithm sign bits renement bitsand signicance map coding bits  The last contextcan be subdivided into four subcontexts single coecients set D set L and sons  We have thus sixdierent contexts  At this point we consider somerelationships between the wavelet coecients in thecollection of spatial orientation trees  For this reason we identify subcontexts dependent on the signicance value of the father or of the brothers ofthe node or set we are analyzing  This leads toa modeling of the SPIHT source with  dierentcontexts It is important to note that we entropy code alsothe renement bits contrary to the original SPIHTapproach because as already seen the subbandcoecient histograms of each bitplane interval isunbalanced towards lower values and so it is moreprobable that a coecient lies in the inferior halfinterval rather than in the superior one  Arithmeticcoding permits to obtain an increment of the PSNRof    dB on threedimensional data at a rate0.1 0.2 0.3 0.4 0.532343638404244Rate (bit per pixel)PSNR (dB)With Arithmetic CodingWithout Arithmetic CodingFigure  Performance improvement by the use ofcontext based arithmetic coding ranging from   to   bpp as shown in Fig   EXPERIMENTAL RESULTSWe test our compression scheme using the samevolume CT SKULL xx voxels used in  In Fig  we show the PSNR calculated oneach slice in z direction for two rate of compression   and   bpp  In this case we used the 	wavelet lters on xy and the  ones along thez direction  The obtained results are better bothfor the mean PSNR on the whole volume and forthe homogeneity of the PSNR between successiveslices as shown in Tab  for the slice codingunit at rate of   and   bpp  The three methodsare compared in whole volume PSNR worst slicePSNR and PSNRoscillation range a measure ofthe PSNR dierences between consecutive or nearslices The increment in the mean PSNR is obtainedthanks to the improvements to the SPIHT algorithm and to the context modeling used in thearithmetic coder  It also benets from the useof a dierent wavelet transform  Moreover theachieved reduction of the oscillation between nearslices depends primarily on the selected wavelet Integer wavelet transforms are used in  and in order to guarantee the possibility of lossless compression of the biomedical data but in lossy condition they work worse  Besides we argue thatbpp DEZW  DSPIHT  IDSPIHT     	                   	  	             Table   Mean PSNRdB worst slice PSNR andoscillation range on  slice of the CT SKULLvolume  coded at   and   bpp SPIHT coding becomes inecient if pushed to lossless compression that biomedical data are noisyand so perfect lossless compression is not mandatory as it may seems and that uncontrolled oscillations of PSNR values between consecutive slice maylead to objectionable artefacts when compression islossy  0 20 40 60 80 100 1203032343638404244464850Slice NumberPSNR (dB)0.5 bpp 0.1 bpp Figure  Lossy coding of CT SKULL PSNR onD slices for   and   bpp  CONCLUSIONSIn this paper we proposed an extension of SPIHTbased techniques to the D case and suggested howto improve the performance of the SPIHT algorithm without adding any computational cost  Wealso introduced a set of D contexts in order toobtain a highly performing arithmetic coder  Weshowed the eectivenes of our approach by appying it to a biomedical test volume and comparingit with respect to others similar works  Based onthe obtained experimental results we suggest notto use integer wavelet lters when this makes worsethe objective quality or leads to unpredictable oscillations of the interslice PSNR  In conclusion iflossy compression of biomedical data were acceptable as it is reasonable in some clinical contextse g  teleradiology long term storage archives theproposed D data compression technique could beuseful to code not too anisotropic volumes 	  REFERENCES  J Wang HK Huang Medical Image Compression by Using ThreeDimensional Wavelet Transformation IEEE Trans  Medical Imag  	 Aug   A Signoroni R LeonardiDiagnostic Compression of Biomedical Volumes in EUSIPCO  Sep  A Bilgin G Zweig MW Marcellin Threedimensional image compression with integerwavelet transforms Appl  Opt  	 Apr  Z Xiong X Wu DY Yun and WA PearlmanProgressive coding of medical volumetric datausing threedimensional integer wavelet packettransform in VCIP SPIE vol Jan  M Antonini M Barlaud P Mathieu IDaubechies Image coding using wavelet transformIEEE Trans Image Proc  	  Apr  MJ Tsai J Villasenor F Chen Stackrun image coding IEEE Trans  Circ and Sys for VideoTech  	  Oct  A Said and WA Pearlman A New Fast andEcient Image Codec Based on Set Partitioning in Hierarchical Trees IEEE Trans  Circ andSys for Video Tech  	  Jun  A Moat RM Neal IH Witten ArithmeticCoding Revisited ACM Trans  on InformationSystems 	  July   ASignoroni Representation and CompressionMethodologies for Biomedical Volumes PhD thesis University of Bresciain Italian Feb

Improving SPIHT-based Compression of Volumetric Medical Data

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