A New Adaptive Medical Image Coding with Orthogonal Polynomials

Transcription

1 Ieraioal Joural of Compuer Applicaios ( ) Volume 46 No., May A New Adapive Medical Image Codig wih Orhogoal Polyomials Krishamoorhy R Deparme of CSE Aa Uiversiy of Techology - Tiruchirappalli Tiruchirappalli, Tamiladu, Idia 6 4 Rajavijayalakshmi K Deparme of CSE Aa Uiversiy of Techology - Tiruchirappalli Tiruchirappalli, Tamiladu, Idia 6 4 ABSTRACT I his paper, ew adapive medical image codig echique based orhogoal polyomials rasformaio is proposed. The ipu image is firs applied wih he proposed orhogoal polyomials based modified zero crossig algorihm for edge deecio sice i is o sesiive o oise ad surface irregulariies. The he sca fillig algorihm is used o separae he foregroud ha coais he mos impora iformaio of medical image from he backgroud regio. The orhogoal polyomials based rasform codig echique is applied o foregroud regio for lossless ecodig ad o backgroud regio for lossy ecodig. The proposed work uses variable quaizaio o maiai differe qualiy levels for eire image codig ad preserve he mos impora feaures ha coaied i he foregroud regio of medical image. The experime resuls of he proposed echique shows ha a higher compressio raio is achieved for codig of medical images wih lower compuaioal complexiy whe compared wih exisig echiques. Geeral Terms Image codig. Keywords Edge segmeaio, sca fillig algorihm, orhogoal polyomials based rasform codig.. INTRODUCTION Medical imagig [,] plays a sigifica role i coemporary healh care, boh as a ool i primary diagosis ad as a guide for surgical ad herapeuic procedures. Wih icreasig umber of paie daa, he compressio echiques for digial rasmissio ad sorage of medical images have become a ecessiy [3]. Medical image compressio is cosraied by he fac ha mos radiologiss are o willig o base a diagosis o a image ha has bee compressed i a lossy way. This is parially due o legal reasos (depedig o he correspodig coury's laws) ad parially due o he fear of misdiagosis because of los daa i he compressio procedure [4]. Therefore, oly lossless echiques are acceped, which limis he amou of compressio o a facor of abou 3 (i coras o facors of or more achievable i lossy schemes). Sice he compressio rae i lossless model is poor, here is a eed for efficie ad widely acceped echiques for medical image compressio. A possible soluio o his dilemma is o offer he image compressio echiques which allow a image o be selecively compressed. The pars of he image ha coai crucial iformaio (called foregroud regio) are compressed i a lossless way whereas regios coaiig uimpora iformaio (called backgroud regio) are compressed i a lossy maer. This leads o cosiderably higher compressio raios as compared o pure lossless schemes while criical iformaio is preserved. The lossless compressio scheme reproduces he same origial daa wihou ay loss of iformaio ad he lossy compressio scheme produces he approximaio of he origial daa a a higher compressio rae. The echiques i he ar of compressig he image daa ca be classified io wo caegories: i) ime-domai (or space domai) ecodig ad ii) rasform domai codig. The ime domai echiques ha appear pracical are mosly of he predicio-compressio ype. This icludes schemes like dela modulaio ad differeial pulse code modulaio [5]. The rasform codig schemes are proved o be a effecive image compressio scheme ad is he basis of all world sadards for lossy compressio [6]. These rasforms beig uiary, coserve he sigal eergy i he rasform domai, bu ypically mos of his eergy is coceraed i relaively few samples which are usually he lower frequecy samples. The simple ad powerful class of rasform codig is liear block rasform codig, where he eire image is pariioed io a umber of o-overlappig blocks ad he he rasformaio is applied o yield rasform coefficies. This is ecessiaed because of he fac ha he origial pixel values of he ipu image are highly correlaed. Compressio is achieved by cosiderig he high eergy samples o be sufficie for recosrucio subseque o rasmissio, sorage or processig. The ieraioal compressio sadards JPEG [7] ad JPEG [8] use he Discree Cosie Trasformaio [9,] ad wavele rasform [,] respecively for image codig. May medical image codig sysems have bee developed boh i spaial domai [3-7] ad i rasform domai [8- ]. The rasform based codig echiques provides efficie reducio of he high redudacy ad achieves higher compressio raio ha he spaial domai echiques. I [8], he selecive image compressio echique ha ecodes he Regio of Ieres (ROI) i lossless mode ad remaiig regio usig loss compressio such as wavele ad DCT based coders. The wavele based medical image codig algorihms which modifies he origial SPIHT ad EBCOT echiques o provide ROI codig feaure for chromosome images is repored by Zhogmi liu e. al.[9]. The applicaio of 3-D Harley rasform for ecodig he medical images is described i []. The 3-D medical image compressio usig 3-D wavele coders is preseed i [], wherei he four symmeric ad decoupled wavele rasforms are used i firs sage ad 3-D SPIHT, 3-D SPECK, 3-D BISK are used i secod sage of medical image compressio. The ECG sigal compressio algorihm preseed i [], uses modified Embedded Zeroree Wavele (EZW) codig algorihm ad repored beer resuls whe comparig wih radiioal EZW algorihm. 5

2 Ieraioal Joural of Compuer Applicaios ( ) Volume 46 No., May Hece a medical image codig echique ha provides higher compressio raio while reaiig impora iformaio is ecessiaed, a ew low complexiy orhogoal polyomials based lossy o lossless medical image codig echique is proposed i his paper. The crucial iformaio prese i he medical images is separaed as foregroud regio from he backgroud regio wih he proposed edge based segmeaio algorihm ad sca fillig algorihm. Sice he hresholdig ype edge deecio mehods is sesiive o oise ad surface irregulariies, he edge deecio hrough he ideificaio of zero crossig based o orhogoal polyomials is proposed i his work. Afer segmeaio, he foregroud regios are ecoded losslessly ad backgroud regios are ecoded i lossy maer wih he proposed orhogoal polyomials based rasform codig echique. This paper is orgaized as follows: The orhogoal polyomials model for he proposed codig is preseed i secio. The basis operaors of he orhogoal polyomials based rasformaio are give i secio. The proposed edge deecio algorihm ad rasform codig echique based o orhogoal polyomials are preseed i secio 4 ad 5 respecively. The measureme of performace is give i secio 6. The experimeal resuls of he proposed codig ad heir compariso wih exisig echique are preseed i secio 7 ad he coclusio is preseed i secio 8.. ORTHOGONAL POLYNOMIALS MODEL I order o devise a rasform codig for lossless image coder, a liear -D image formaio sysem is cosidered aroud a Caresia coordiae separable, blurrig, poi spread operaor i which he image I resuls i he superposiio of he poi source of impulse weighed by he value of he objec fucio f. Expressig he objec fucio f i erms of derivaives of he image fucio I relaive o is Caresia coordiaes is very useful for aalyzig he image. The poi spread fucio M() ca be cosidered o be real valued fucio defied for () X Y, where X ad Y are ordered subses of real values. I case of gray-level image of size ( ) where X (rows) cosiss of a fiie se, which for coveiece ca be labeled as {,,,-}, he fucio M() reduces o a sequece of fucios. M ( i, ) = ui(), i, =,,, - () The liear wo dimesioal rasformaio ca be defied by he poi spread operaor M() (M(i, ) = ui()) as show i equaio ()., M,xM,yI x,ydxdy xx yy () Cosiderig boh X ad Y o be a fiie se of values {,,,, }, equaio () ca be wrie i marix oaio as follows i j M M I where is he ouer produc, ij are marices arraged i he dicioary sequece, I is he image, ij are he coefficies of rasformaio ad he poi spread operaor M is u u u u M u u u u u We cosider a se of orhogoal polyomials u (), u (),, u - () of degrees,,,, - respecively o cosruc he polyomial operaors of differe sizes from equaio (4) for (3) (4) ad i = i. The geeraig formula for he polyomials is as follows. u i+ () = ( ) u i () b i () u i- () for i, (5) u () =, ad u () =, where ui,ui u i b i ad u i,ui u i Cosiderig he rage of values of o be i = i, i =,, 3,,, we ge i i i, 44i b We ca cosruc poi-spread operaors M of differe size from equaio (4) usig he above orhogoal polyomials for ad i = i. For he coveiece of poi-spread operaios, he elemes of M are scaled o make hem iegers. 3. ORTHOGONAL POLYNOMIALS BASIS For he sake of compuaioal simpliciy, he fiie Caresia coordiae se X, Y is labeled as {,, 3}. The poi spread operaor i equaio (3) ha defies he liear orhogoal rasformaio for image codig ca be obaied as M M, where M ca be compued ad scaled from equaio (4) as follows. ux ux ux M ux ux ux = (6) u x u x u x The se of polyomial basis operaors O ij ( i, j -) ca be compued as O ij = û i û j where û i is he (i + ) s colum vecor of M. The complee se of basis operaors of sizes ( ) ad (3 3) are give below. Polyomial basis operaors of size ( ) are O, O, O, O Polyomial basis operaors of (3 3) are O 3, O 3, O 3, O 3, O 3, O 3, 6

3 Ieraioal Joural of Compuer Applicaios ( ) Volume 46 No., May O 3, O 3 4 O 3, I is also proved ha he se of ( ) polyomial operaors forms a basis, i.e i is complee ad liearly idepede. The followig symmeric fiie differeces for esimaig parial derivaives a (x,y) posiio of he gray level image I are aalogous o he eigh fiie differece operaors O ij s excludig O oo. I y I x I y I x ad so o. I geeral, i j i j x y i j = [ I( x i, y ) I( x i, y )] i = [ I( x,y i ) I( x,y i )] i [ I( x i, y ) I( x i, y ) I( x i, y )] i [ I( x, y i ) I( i O ij ad i ) I( x, y i )] I, ( O ij, I ) ij, i.j i j (8) i j x y where idicaes he arrageme i dicioary sequece ad ' (, ) idicaes he ier produc ad ij are he coefficies of he liear rasformaios defied as follows. ' ij = M I (9) where M is he -D poi spread operaor defied as M = M M The orhogoal rasformaio defied by he orhogoal sysem is M complee. A orhogoal sysem H by ormalizig M is obaied as follows H M ( M M ) Cosider he followig orhogoal rasformaios (7) Z H I ( M M ) M I ( M M ) () Sice H is uiary, I H Z where M () ( M M ) ij O ij i j As per equaio (), he image regio I ca be expressed as a liear combiaio of he 9 basis operaors of which O oo is he local averagig operaor ad he remaiig 8 are fiie differece operaors. From his he compleeess relaio or Bessel s equaliy is obaied as follows. ( I, I ) ( Z, Z )i.e., I ij Z i j i j 4. EDGE SEGMENTATION BASED ON ORTHOGONAL POLYNOMIALS I his secio, a edge deecio mehod based o ideifyig he zero crossig i he secod direcioal derivaives of he image is proposed for moochrome images. Afer deecig he edges, he sca lie algorihm is applied o segme he foregroud ad backgroud regio for he proposed ecoder of he medical image. The compuaioal approach for deecio of zero-crossig i he secod direcioal derivaive by usig he proposed polyomials operaor is preseed. Le he image fucio be I(), he he firs order derivaive is give by, I I I ( ) si cos () x y ad he secod direcioal derivaive is give by I I I I ( ) si si cos cos (3) x y x y where y a x Usig equaio (8), we obai I si cos si cos (4) Fially, he expressio for he secod direcioal derivaive i erms of he proposed differece operaor becomes, I ( ) (5) A edge poi ca be cocluded if he image regio uder aalysis has sufficie gradie ad is secod direcioal derivaive has a egaive slope i.e., a zero crossig. The algorihm for deecio of edges i medical images by usig his mehod is give below: Algorihm: Edge deecio usig modified zero crossig algorihm ij 7

4 Ieraioal Joural of Compuer Applicaios ( ) Volume 46 No., May Ipu : Medical image of size (image_widh image_heigh) Oupu: Edge deeced image Seps: Begi. Repea i h loop from o image_widh do begi Repea j h loop from o image_heigh) do begi. Exrac a (3 3) block [I] cered a (i+,j+) 3. Compue ' M T [ I ][ M where [M]= ] 4. Esimae he gradie ' I ( ) 5. If (gradie I T ) go o ed 6. Compue secod direcioal derivaive, I 7. If ( <) mark he edge poi a (i+, j+). ed ed Ed Oce he edge pois are ideified wih he proposed zero crossig algorihm he resula image is deoed as a wo dimesioal marix E of size (image_widh image_heigh). The sca lie algorihm is he applied i boh horizoal ad verical direcio ad he resuls are combied o ge he foregroud ad backgroud medical image regio. The horizoal scaig sars from lef (value ) o righ (value image_widh) o fid he o-zero value i E i,j ad se he colum value j as he sarig colum k. Nex, scas he marix E from righ (image_widh) o lef () o fid he righ mos edge pixel ad se he j h edig colum value as l. The fill he lie from E i,k o E i,l wih value ad his ieraio is repeaed for all he rows i he image o ge he horizoal filled image. The similar procedure is applied from op o boom wih values from o image_heigh ad he verical filled image is obaied. Boh he horizoal ad verical image is he combied by logical AND operaio ad he resula biary image is obaied wih foregroud regios deoed by ad backgroud regio deoed by. 5. PROPOSED LOSSY TO LOSSLESS MEDICAL IMAGE CODING BASED ON ORTHOGONAL POLYNOMIALS The ipu medical image o be coded is divided io o overlappig blocks of size ( ) ad is classified as foregroud regio, if 5% or above he ( ) pixel values are ideified as i machig wih he correspodig biary image oherwise i is classified as backgroud regio. Oce he image regio ( ) is classified, he orhogoal polyomials based rasform coder is applied o ecode he foregroud regio i lossless mode ad backgroud regio i lossy mode wih differe quaizaio levels. The image regio ( ) is applied wih orhogoal polyomials based rasformaio(opt) as described i secio II ad he rasformed coefficies are quaized usig a quaizaio marix whose formula, as i JPEG is give below: OPT( i, j ) Quaized value(i, j)=roud Quaum( i, j ) ' ' ' ' ' ' ' I ( x, y) ' ' I (6) where OPT (i, j ) is rasform coefficie marix obaied wih he orhogoal polyomials rasformaio. The quaum value marix Quaum (i, j ) is obaied hrough a ieger, called qualiy_facor. Depedig upo he requireme of he qualiy of recosruced image vis-à-vis compressio raio, he qualiy_facor ca be made adapive ad be specified by he user. The relaioship bewee Quaum(i, j ) ad he qualiy_facor is Quaum (i, j ) =+((+i+j*qualiy_facor). The qualiy_facor which is a user ipu is geerally i he rage o 5, ad specifies he quaum value, for every eleme posiio i he origial polyomial rasform coefficie marix. The qualiy_facor is chose i such a way ha i ca discard higher frequecy coefficies elegaly. Tha is, whe he qualiy is high, he quaum value correspodig o he higher frequecy coefficie sample posiios shall be high so ha he quaized value ca be zero. Thus he quaum value idicaes wha ha he sep size is goig o be for a eleme i he complee rediio of he picure, wih values ragig from o 5. For ecodig he foregroud regio, he qualiy_facor value is chose as which ecodes he image i lossless mode ad gives perfec recosrucio of he image. Similarly for ecodig he backgroud regio, he qualiy_facor rages from o 5 which ecodes he image i lossy mode givig higher compressio raio wih sigifica reducio i recosruced image qualiy. The quaized rasformed coefficies of boh regios are he subjeced o eropy ecodig usig variable legh codig. For his purpose, he quaized rasform coefficies are reordered usig zigzag scaig o form a D sequece. Due o he fac ha DC coefficies of he proposed orhogoal polyomials based codig have high magiude ad he DC values of eighborig blocks are o differig subsaially, he DC values are subjeced o differece pulse code modulaio (DPCM). The firs eleme of he zigzag sequece represes he differece pulse code modulaed DC value ad amog he remaiig AC coefficies, he o-zero AC coefficies are huffma coded usig variable legh code (VLC) ha defies he value of he coefficie ad he umber of precedig zeros. Sadard VLC ables specified i he JPEG baselie sysem are used for his purpose. The side iformaio bi as for foregroud regio ad for backgroud regio is se alog wih ecoded bisreams. Sice he huffma coded biary sequeces are isaaeous ad uiquely decodable, he compressed image ca be decompressed easily i a simple look-up able maer. The rearraged array of rasform coefficies is reordered io wo dimesioal block from he oe dimesioal regeeraed zigzag sequece wih dequaizaio, afer akig care of DPCM DC coefficies ad we recosruc he sub image uder aalysis by usig he polyomials basis operaors as defied i Secio 3. The deailed algorihm of proposed lossy o lossless image coder is described hereuder: Algorihm for proposed lossy o lossless image coder based o orhogoal polyomials (LLICOPT): Ipu : Medical image ad correspodig biary image. Oupu Ecoded image wih proposed LLICOPT. 8

5 Ieraioal Joural of Compuer Applicaios ( ) Volume 46 No., May Seps:. Pariio he ipu image io ( ) blocks ad classify i eiher as foregroud regio or backgroud regio as described i his secio.. Compue he orhogoal polyomials rasformed coefficies as i j ( M M ) I as descried i secio. 3. Quaize he rasformed coefficies wih qualiy_facor value as if he regio is classified as foregroud regio, oherwise ecode he backgroud regio wih qualiy_facor value rages from o 5 as user ipu as give i equaio (6). 4. Rearrage he quaized rasformed coefficies i oe dimesioal sequece usig zig-zag scaig. 5. Ecode he DC coefficie usig DPCM coder ad he remaiig AC coefficies usig huffma coder. 6. Repea he above process uil all he blocks i he ipu image have bee ecoded. Decodig is he reverse process of ecodig ad is doe as a simple look up able maer. Firs eropy decodig is applied o he compressed bi sreams ad he resuls are muliplied wih differe quaum values for de-quaizig he foregroud regio ad backgroud regio separaely alog wih he side iformaio. The iverse rasform is he applied wih orhogoal polyomials basis operaor as described i secio 3 ad he recosruced image is obaied. ecoded losslessly ad backgroud regios are ecoded i lossy way wih he proposed orhogoal polyomials based rasform coder as described i secio 5. For foregroud regio, he qualiy_facor is se as ad for backgroud regio he qualiy_facor rages from o 5 ad he resuls are preseed i able. For a qualiy _ facor, he proposed LLICOPT codig scheme gives a compressio raio of 66.34% wih a PSNR of 46.76dB for he mammogram image. For he same qualiy _ facor, he proposed codig achieves a compressio raio of 64.39% wih a PSNR value of 47.5dB for he X-ray image. For he qualiy _ facor value of 5, proposed LLICOPT codig achieves a compressio raio of 73.95% wih a PSNR value 45.dB for mammogram image ad 7.78% compressio raio wih a PSNR value of 46.33dB for X-ray image. The recosruced images correspodig o he origial images i fig..(a)-(d) are preseed i fig.3(a)-(d) wih he proposed algorihm. For low qualiy ecodig wih he qualiy _ facor of 5, he proposed algorihm achieves a compressio raio of 85.7% wih a PSNR value of 38.7dB for he mammogram image ad 8.65% compressio raio wih PSNR value of 39.86dB for X-ray image. 6. MEASURE OF PERFORMANCE The performace of he proposed lossy o lossless medical image codig algorihm is repored by compuig he peak sigal-o-oise raio (PSNR), as 55 PSNR log (7) e ms where he average mea-square error e ms, is a very useful measure as i gives a average value of he eergy los i he lossy compressio of he origial image ad is give by e ms NM N M f (i, j ) g( i, j ) i j (8) where f (i, j ) ad g (i, j ) represe he origial ad reproduced color images of size (N M) respecively. The PSNR is measured i decibels (db). (a) Mammogram (c) CT sca (b) X-ray (d) MRI image 7. EXPERIMENTS AND RESULTS The proposed algorihm has bee esed wih more ha medical images of differe kids such as mammogram, X- ray, CT-sca ad MRI images. Some sample medical images which are of size (56 56) wih pixel values i he rage (-55) are show i fig..(a)-(d). The image are applied wih he proposed orhogoal polyomials based modified zerocrossig edge deecio algorihm as described i secio 4 ad he oupus are preseed i fig..(a)-(d) correspodig o he origial images i fig..(a)-d) respecively. The biary imaged wih foregroud ad backgroud regio are obaied usig sca fillig algorihm. The he foregroud regios are Figure Origial medical es images (a) Mammogram (b) X-ray 9

6 Ieraioal Joural of Compuer Applicaios ( ) Volume 46 No., May (c) CT sca (d) MRI image Figure Edge deecio wih proposed modified zero crossig algorihm based o orhogoal polyomials. I order o measure he performace of he proposed echique, he experimes are coduced usig DCT based codig scheme ad he resuls are preseed i able. For a qualiy _ facor, he DCT based codig scheme gives a compressio raio of 57.43% wih a PSNR of 44.76dB for he mammogram image. For he same qualiy _ facor, he DCT based codig scheme gives a compressio raio of 55.8% wih a PSNR value of 45.54dB for he X-ray image. For he qualiy _ facor value of 5, DCT based codig scheme gives a compressio raio of 68.55% wih a PSNR value 4.dB for mammogram image ad 64.6% compressio raio wih a PSNR value of 43.56dB for X-ray image. For low qualiy ecodig wih he qualiy _ facor of 5, he DCT based codig scheme gives a compressio raio of 8.68% wih a PSNR value of 36.7dB for he mammogram image ad 79.5% compressio raio wih PSNR value of 37.6dB for X-ray image. 8. CONCLUSION (a) Mammogram (c) CT sca (b) X-ray (d) MRI image Figure 3 Resuls of proposed codig scheme whe qualiy_facor is 5 I his paper, ew medical image codig echique based o orhogoal polyomials is proposed. The edges i he medical images are firs deeced wih he proposed orhogoal polyomials based modified zero crossig algorihm. The criical iformaio i he medical images iside he ouer edges are ideified as foregroud regio ad he remaiig porio are ideified as backgroud regio usig sca fillig algorihm. Boh regios are ecoded usig variable quaizaio wih proposed orhogoal polyomials based rasform codig echique. Sice he discrimiae iformaio i he medical images is he foregroud regio ad is ecoded losslessly, a hudred perce accuracy is achieved wih he proposed echique for diagosig he problem while a he same ime a higher compressio raio is achieved by lossy compressio of backgroud regio. Table 6.5 Compressio raio(%) ad PSNR(dB) values obaied for various qualiy_facors wih proposed LLICOPT algorihm. QF Proposed LLICOPT based codig scheme Mammogram X-ray CT-sca MRI image CR PSNR CR PSNR CR PSNR CR PSNR

7 Ieraioal Joural of Compuer Applicaios ( ) Volume 46 No., May Table 6.6 Compressio raio (%) ad PSNR (db) values obaied for various qualiy_facors(qf) wih proposed algorihm usig DCT based codig scheme. QF Proposed algorihm usig DCT based codig scheme Mammogram X-ray CT-sca MRI image CR PSNR CR PSNR CR PSNR CR PSNR REFERENCES [] R.A. Greees, J.F. Brikley. 99. Radiology sysems, i: E.H. Shorliffe, L.E. Perreaul (Eds.), Medical Iformaics Compuer Applicaios i Healh Care, Addiso-Wesley, Readig, MA. [] A. Macovski, 983. Medical Imagig Sysems, Preice- Hall, Eglewood Cliffs, NJ. [3] G.Barlas, S.Kosomaolakis ad S.C.Orphaoudakis.. DICOM image compressio usig a hierarchy of predicors. IEEE Ieraioal Coferece o Egieerig i Medicie ad Biology Sociey, Vol.3, [4] S. Wog, L. Zaremba, D. Goode ad H.K. Huag Radiologic image compressio - a review. Proceedigs of he IEEE Trasacios, Vol., [5] R. Schidler, Dela modulaio, IEEE Trasacios o Specrum, 97, Vol.7, No., [6] Jai A.K. 98. Image Daa Compressio: A Review. Proceedigs of IEEE, Vol. 69, [7] G.K. Wallace. 99. The JPEG Sill Picure Compressio Sadard. Commuicaios of ACM, Vol.34, [8] Charilaos Chrisopoulos, Ahaassios Skodras ad Touradj Ebrahimi, The JPEG Sill Image Codig Sysem: A Overview, IEEE Trasacios o Cosumer Elecroics,, Vol. 46, 3-7. [9] N. Ahamed.T. Naaraja ad K.R. Rao., Discree Cosie Trasform, IEEE Trasacios o Compuer, 974, Vol. 3, [] R.C. Reiiger ad J. Gibso, Disribuio of - Dimesioal DCT Coefficies for Images, IEEE Trasacios o Commuicaios, 983, Vol.3, [] M. Aoii, M.Barlaud, P.Mahieu ad I.Daubechies, Image Codig usig Wavele Trasform, IEEE Trasacios o Image Processig, 99, Vol., 5-. [] M. D. Adams ad F. Kosseii, Reversible Ieger- To-Ieger Wavele Trasforms for Image Compressio: Performace Evaluaio ad Aalysis, IEEE Trasacios o Image Processig,, Vol.9, -4. [3] W.Philips, S.Va Assche D.De Rycke ad K.Deecker, Sae-of-he-ar echiques for lossless compressio of 3D medical image ses, Compuerized Medical Imagig ad Graphics,, Vol. 5, No., [4] Vicor Sachez Paos Nasiopoulos ad Rafeef Abugharbieh, Novel Lossless FMRI Image Compressio based o Moio Compesaio ad Cusomized Eropy Codig, IEEE Trasacios o Iformaio Techology i Biomedicie, 9, Vol.3, No.4, [5] Vicor Sachez, Rafeef Abugharbieh, ad Paos Nasiopoulos. 9. 3D Scalable lossless compressio of medical images based o global ad local symmerics. IEEE Ieraioal coferece o Image Processig, [6] Gerald Schaefer, Roma Sarosolski ad Shao Yig Zhu. 5. A evaluaio of lossless compressio algorihms for medical ifrared Images. IEEE Egieerig i Medicie ad Biology 7h Aual Coferece, [7] Joaha Taque ad Claude Labi.. Near-lossless ad scalable compressio for medical imagig usig a ew adapive hierarchical orieed predicio. IEEE Ieraioal Coferece o Image Processig, [8] Alfred Bruckma ad Adreas Uhl, Selecive medical image compressio echiques for elemedical ad archivig applicaios, Compuers i Biology ad Medicie,, Vol.3, No.3,

8 Ieraioal Joural of Compuer Applicaios ( ) Volume 46 No., May [9] Zhogmi Liu, Jiapig Hua, Zixiag Xiog, Qiag Wu, ad Keeh Caslemad.. Lossy-o-Lossless ROI codig of chromosome images usig modified SPIHT ad EBCOT. IEEE Ieraioal Symposium o Biomedical Imagig, [] R.Shyam Suder, C.Eswara, N.Sriraam, Medical image compressio usig 3-D Harley rasform, Compuers i Biology ad Medicie, 6, Vol.36, No.9, [] N.Sriraam ad R.Shyamsuder, 3-D medical image compressio usig 3-D wavele coders, Digial Sigal Processig,, Vol., No., pp. 9. Gülay Tohumoglu ad K. Erbil Sezgi, ECG sigal compressio by muli-ieraio EZW codig for differe waveles ad hresholds, Compuers i Biology ad Medicie, 7, Vol.37, No., 73 8