Volume, No. 4, November 0 Joural of Global Research i Computer Sciece RESEARCH PAPER Available Olie at www.jgrcs.ifo PERFORMANCE ANALYSIS OF LOSSY COMPRESSION ALGORIHMS FOR MEDICAL IMAGES Dr. V. Radha* ad Pushpalakshmi * Professor, Departmet of Computer Sciece Aviashiligam Deemed Uiversity for Wome, Coimbatore, Idia. radharesearch@yahoo.com Research Scholar Aviashiligam Deemed Uiversity for Wome, Coimbatore, Idia. mppuspalakshmi@gmail.com Abstract: Image compressio addresses the problem of reducig the amout of data required to preset a digital image with acceptable image quality. he uderlyig basis of the reductio process is the removal of redudat data. Medical image compressio plays a key role as healthcare idustry move towards filmless imagig ad goes completely digital. he problem of medical image compressio is a cotiuig research field ad most of the researches beig proposed cocetrate either o developig a ew techique or ehace the existig techiques. he medical commuity has bee reluctat to adopt lossless methods for image compressio. he mai goal has bee to produce a exact replica of the origial image, sufferig high file size. Oly recetly, attetio to use lossy image compressio, which maximizes compressio while maitaiig cliical relevace data, has bee probed. Four solutios to aswer the above problem statemet have bee selected, amely, Block rucatio Codig (BC), Discrete Cosie rasformatio (DC), Discrete Wavelet rasformatio (DW) ad Sigular Value Decompositio (SVD) were selected because of their predomiat place i geeral image processig field. Various experimets were coducted to aalyze the performace of the four image compressio models o medical image compressio. Keywords: Medical Image Compressio, Block rucatio code, Discrete Cosie rasformatio, Discrete Wavelet rasformatio Sigular Value Decompositio, Lossy Compressio. rasformatio (DC), Discrete Wavelet rasformatio INRODUCION (DW) ad Sigular Value Decompositio (SVD). hese techiques were selected because of their predomiat place i geeral image processig field. he developmet of moder equipmets ad commuicatio devices i healthcare idustry has made it possible to take specialty healthcare to the rural ad remote populatio of a coutry. he future of healthcare idustry is shaped by teleradiology ad techologies such as telemedicie []. Patiet iformatio, which may iclude patiet details, treatmet history, images of previous tests, etc., plays a importat role i these techologies. I particular, image data acquired from various medical equipmets like X-Ray, C, MRI, etc. is icreasigly trasmitted through World Wide Web, telephoe, mobile, WANs, etc. All these systems face two commo problems, high storage requiremet ad image quality. A solutio proposed i such situatio is image compressio, which is defied as a techique that ivolves methods to reduce the size of the image data files while retaiig ecessary importat iformatio []. It is a area which has foud use i several applicatios like the Iteret, photography ad medical idustry. May works have bee proposed i the area of photographic image compressio, compoud image compressio, graphics, etc., but whe it comes to medical images, a compressio requiremet varies ad therefore the amout of work proposed reduces sigificatly. I geeral, the medical commuity uses lossless compressio techiques, where the image quality is a exact replica of the origial image. hese techiques produce good image quality but suffer from huge file size. Oly recetly, attetio to use lossy image compressio to maximizes compressio while maitaiig cliical relevace data has bee probed. I this paper, four solutios are compared o their applicability to medical images ad the techique that best suits medical image compressio is idetified. he techiques selected are Block rucatio Codig (BC), Discrete Cosie he paper is orgaized as below: Sectio provided a brief itroductio to the topic. Sectio gives a overview of the related reviews i this area. Sectio 3 discusses the methodology behid each techique, while Sectio 4 presets the result of various experimets coducted. Sectio 5 cocludes ad summarizes the work with future research directios. REVIEW OF LIRAURE his sectio reviews work related to medical image compressio. Lossy compressio approach for medical images started to gai popularity i medical domai oly after 000. he classical examples of popular lossy compressio algorithms are Joit Photographic Expert Group (JPEG) [3] ad a more recet stadard JPEG000 [4]. hese algorithms are based o Discrete Cosie rasformatio (DC) for JPEG ad Discrete Wavelet rasform (DW) [5] for JPEG000. Lossy predictive codig is also used for the ear-lossless compressio whe the degree of imposed degradatio is limited. Lossy predictive codig assumes that the predictio error is ot ecoded precisely but quatized, thereby causig mior errors whe the image sample is recostructed. his techique is used i JPEG-LS ear-lossless mode, for example. Aother approach for lossy compressio is, istead of trasformig the whole image, to separately apply the same trasformatio to the regios of iterest i which the image could be divided accordig to a predetermied characteristic. JGRCS 0, All Rights Reserved 46
Oe importat such characteristic of medical images is texture. More specifically, texture aalysis of these images ca lead to very sigificat results cocerig real tissue motio ad thus, ca result i improved diagosis [6]. he goal of such a lossy compressio methodology that aims at maximizatio of the overall compressio ratio is to compress each regio separately with its ow compressio ratio, depedig o its textural sigificace, so as to preserve textural characteristics. With regard to cliically relevat regio ecodig, ot much has bee published. I 994, [7] made use of regios of iterest usig subbad aalysis ad sythesis orvolumetric datasets usig wavelets. hey followed up this work i [8] by usig structure preservig adaptive quatisatio methods as a meas of improvig quality for compressio rates i the regios of iterest. But all of their effort was o lossy approaches. Storm ad Cosma [9] developed a regio based codig approach. hey discussed two approaches: oe uses differet compressio methods i each regio such as cotour-texture codig ad subbad decompositio codig, ad the other uses the same compressio method i each regio such as the discrete cosie trasform but with varyig compressio quality i each regio such as by usig differet quatisatio tables. hey used two multiresolutio codig schemes: wavelet zerotree codig ad the S-trasform, ad cosidered oly 8 bit images. I their implemetatio, the regios of iterest were selected maually. COMPRESSION ECHNIQUES Four techiques are selected for testig its applicability i medical image compressio domai. hey are (i) Block rucatio Codig (BC) (ii) Discrete Cosie rasformatio (DC) (iii) Discrete Wavelet rasformatio (DW) ad (iv) Sigular Value Decompositio (SVD). he workig is explaied i the followig sectios. A. BC Block rucatio Codig (BC) is a lossy momet preservig quatizatio method for compressig digital gray-level images. Its advatages are simplicity, fault tolerace, the relatively high compressio efficiecy ad good image quality of the decoded image. he BC algorithm is a lossy fixed legth compressio method that uses a Q level quatizer to quatize a local regio of the image. he quatizer levels are chose such that a umber of the momets of a local regio i the image are preserved i the quatized output. I its simplest form, the objective of BC is to preserve the sample mea ad sample stadard deviatio of a grayscale image. Additioal costraits ca be added to preserve higher order momets. For this reaso BC is called as a block adaptive momet preservig quatizer. he priciple used by the block trucatio codig (BC) method ad its variats is to quatize pixels i a image while preservig the first two or three statistical momets. he algorithm begis by dividig a image ito blocks (4 4 or 8 8 pixels). Assumig that a block cotais pixels with itesities p through p, the first two momets are the mea ad variace, ca be calculated usig Equatios () ad (), from which the stadard deviatio of the block ca be calculated (Equatio 3). p = p () i i= p = p () i i= σ = p p (3) he priciple of the quatizatio is to select three values, a threshold p thr, a high value p, ad a low value p. Each pixel is replaced by either p or p, such that the first two momets of the ew pixels (i.e., their mea ad variace) will be idetical to the origial momets of the pixel block. he rule of quatizatio is that a pixel p i is quatized to p if it is greater tha the threshold, ad is quatized to p if it is less tha the threshold (if p i equals the threshold, it ca be quatized to either value). hus, p if p i p p thr (4) i p if pi > pthr Ituitively, it is clear that the mea p is a good choice for the threshold. he high ad low values ca be determied by writig equatios that preserve the first two momets, ad solvig them. he umber of pixels i the curret block that are greater tha or equal to the threshold is deoted by. Similarly, stads for the umber of pixels that are smaller tha the threshold. he sum equal the umber of pixels i the block. Oce the mea p has bee computed, both ad are easy to calculate. Preservig the first two momets is expressed by the two equatios p = p p, Ad the solutios are p = (p ) (p )... (5) p = p σ, p = p σ (6) As these solutios are geerally real umbers, they are rouded to the earest iteger, which implies that the mea ad variace of the quatized block may be somewhat differet from those of the origial block. he solutios located o the two sides of the mea p at distaces are proportioal to the stadard deviatio of the pixel block. B. DC he Discrete Cosie rasform (DC) is a mathematical trasformatio techique that is used to covert a spatial represetatio of data ito a frequecy represetatio. A data i the frequecy domai cotais the same iformatio as that i the spatial domai. he order of values obtaied by applyig the DC is coicidetally from lowest to highest frequecy. his feature ad the psychological observatio that the huma eye ad ear are less sesitive to recogizig the higher-order frequecies leads to the possibility of compressig a spatial sigal by trasformig it to the frequecy domai ad droppig high-order values ad keepig low-order oes. Whe recostructig the data ad trasformig it back to the spatial domai, the results are remarkably similar to the origial sigal. he DC method ca be used to compress both color ad gray scale images. DC is a method is most frequetly used i several areas icludig WWW, idustries, etc. ad this popularity has made the author choose DC as a format to be aalyzed ad compared. he block diagram of the DC image compressor is show i Figure ad the step by step procedure is give below. JGRCS 0, All Rights Reserved 47
. he image is divided ito 8 x 8 blocks of pixels.. Workig from left to right, top to bottom, apply DC to each block. 3. Compress each block through a process called quatizatio 4. he resultig array of blocks that costitute the image is highly compressed ad occupy very small amout of space. 5. Whe desired, the image ca be recostructed through Iverse Discrete Cosie rasform (IDC), which is a reverse process of compressio. C. DW Figure. Block Diagram of DC Compressio he wide spread attetio o digital image compressio has attracted the attetio of several researchers ad academicias, leadig to the stadardizatio of various digital image compressio algorithms for differet types of images ad applicatios. Existig techiques, despite havig the advatages like simplicity ad satisfactory performace, are ot without shortcomigs. he major disadvatage is the blockig artifacts produced due to the fixed block size limitatio (hakur ad Kakde, 007). his disadvatage ca be overcome by usig a cocept called wavelets, itroduced 0 years ago, which yields a multiscale decompositio ad ca be efficietly coded (Wellad, 003). Over the past several years, the wavelet trasform has gaied widespread acceptace i sigal processig i geeral ad i image compressio research o particular. I geeral, there are three essetial stages i a wavelet trasform-based image compressio system: trasformatio, quatizatio, ad lossless etropy codig. Figure depicts the ecodig ad decodig processes. he oly differet part i the decodig process is that the de-quatizatio takes place ad it is followed by a iverse trasform i order to approximate the origial image. he purpose of trasformatio stage is to covert the image ito a trasformed domai i which correlatio ad etropy ca be lower ad the eergy ca be cocetrated i a small part of the trasformed image. X X INPU DC Quatizatio rucatio ad Zig-Zag scaig Compressed output rasformatio Quatizatio Etropy ecodig Iverse rasformatio Quatizatio stage results i loss of data because it reduces the umber of bits of the trasform coefficiets. Coefficiets that do ot make sigificat cotributios to the total eergy or visual appearace of the image are represeted with a small umber of bits or discarded while the coefficiets i the opposite case are quatized i a fier fashio (Kofidisi et al., 999; Schomer et al., 998). Such operatios reduce the visual redudacies of the iput image (Gozalez ad Woods, 99). he etropy codig takes place at the ed of the whole ecodig process. It assigs the fewest bit code words to the most frequetly occurrig output values ad most bit code words to the ulikely outputs. his reduces the codig redudacy ad thus reduces the size of the resultig bitstream. Dequatizatio Etropy decodig Storage/ Chael Figure. Block diagram of DW based Compressio Scheme D. SVD Sigular Value Decompositio (SVD) is cosidered to be oe of the sigificat topics i liear algebra by may reowed mathematicias. SVD has may practical ad theoretical values, other tha image compressio. Oe special feature of SVD is that it ca be performed o ay real (m,) matrix. It factors A ito three matrices U, S, V, such that, A = USV. Where U ad V are orthogoal matrices ad S is a diagoal matrix. I this research work, the values of SVD are used to perform medical image compressio ad the process is explaied i this sectio. he mai purpose of (SVD) is to factor a image matrix A ito USV. he matrix U cotais the left sigular vectors, the matrix V cotais the right sigular vectors, ad the diagoal matrix S cotais the sigular values. he sigular values to attai this goal are arraged o the mai diagoal as give i Equatio (7) σ σ.σ r > σ r = σ p = 0 (7) where r is the rak of matrix A, ad where p is the smallest of the dimesios m or. here are may properties ad attributes of SVD, some of the properties used with medical image compressio are listed below.. he sigular value σ, σ, σ, are uique, however, the matrices U ad V are ot uique. Sice A A = VS SV ad V diagoalizes A A, it follows that the v j s are the eigevector of A A. 3. Sice AA = USS U, so it follows that U diagoalizes AA ad that the u i s are the eigevectors of AA. 4. If A has rak of r the v j ad v j,, v r form a orthoormal basis for rage space of A, R(A ), ad u j ad u j,, u r form a orthoormal basis for.rage space A, R(A). 5. he rak of matrix A is equal to the umber of its ozero sigular values. Accordig to the property 5 of SVD i sectio 6., the rak of matrix A is equal to the umber of its ozero sigular values. I may applicatios, the sigular values of a matrix decrease quickly with icreasig rak. his propriety allows to reduce the oise or compresses the matrix data by elimiatig the small sigular values or the higher raks. Whe a image is SVD trasformed, it is ot compressed, but the data take a form i which the first sigular value has a great amout of the image iformatio. With this, it is possible to use oly a few sigular values to represet the image with little differeces from the origial. o illustrate the SVD JGRCS 0, All Rights Reserved 48
image compressio process, the followig detail procedures are give below. A USV r = σ iu i v (8) i i= hat is A ca be represeted by the outer product expasio: A = σ u v σ u v σ r u r v r Whe compressig the image, the sum is ot performed to the very last SVs ad the SVs with small eough values are dropped, as they are ordered o the diagoal fashio. he closet matrix of rak k is obtaied by trucatig those sums after the first k terms: A k = σ u v σ u v σ k u k v k (9) () he total storage for k A will be k(m ). he iteger k ca be chose cofidetly less the ad the digital image correspodig to ka will still be very close the origial image. However, the selectio of differet k values will produce differet correspodig image ad with differet memory usage. For typical choices of the k, the storage required for ka will be less the 0 percetage. EXPERIMENAL RESULS he proposed system was vigorously tested with test images to aalyze its performace o compressig medical images. he results obtaied are discussed i this chapter. he images used for this research were 5x5, 8 bits per pixel (bpp) images (Figure 3). All the experimets were coducted usig Petium IV machie with 5MB RAM. he system is evaluated usig the performace parameters, like, Compressio Ratio, Peak Sigal to Noise Ratio (PSNR), Compressio ime ad Decompressio ime. (a) C (b) FOO (c) MRI for the algorithm to perform the ecodig ad decodig algorithm respectively. Peak Sigal to Noise Ratio (PSNR) Peak Sigal to Noise Ratio ratio is ofte used as a quality measuremet betwee the origial ad a compressed image. he higher the PSNR, the better the quality of the compressed, or recostructed image. o compute the PSNR, the block first calculates the mea-squared error usig the followig equatio: [I(m,) I(m,)] M,N MSE = Mx N () I the previous equatio, M ad N are the umber of rows ad colums i the iput images, respectively. he the block computes the PSNR usig the followig equatio: R PSNR = log MSE (3) I the previous equatio, R is the maximum fluctuatio i the iput image data type. For example, if the iput image has a double-precisio floatig-poit data type, the R is. If it has a 8-bit usiged iteger data type, R is 55, etc. For color images with three RGB values per pixel, the defiitio of PSNR is the same except the MSE, which will be the sum over all squared value differeces divided by image size ad by three. ypical values for the PSNR i lossy image ad video compressio are betwee 30 ad 50 db, where higher is better. he PSNR for color images with color compoets, R, G ad B is give as below: PSNR = 55 log MSE(R) MSE(G) MSE(B) 3 ( 4) I the previous equatio, R (=55) is the maximum fluctuatio i the iput image data type. E. Compressio Ratio he result obtaied while aalyzig the compressio ratio of the four models is give i Figure 4. (d) BRAIN (e) CHES (f) KNEE Compressio Ratio Figure 3. est Images he degree of data reductio obtaied as a result of the compressio process is kow as the compressio ratio. his ratio measures the quatity of the compressed data i compariso to the quatity of the origial data. Compressio ratio = origial size/ compressed size () From the above equatio, it is obvious that as the compressio ratio icreases the compressio techique employed is more effective. Compressio ad Decompressio ime Compressio ad decompressio time are the basic measuremets used to evaluate a image compressio system. Compressio ad decompressio time deotes the time take Compressio Ratio (%) 0 90 80 70 60 50 40 30 0 0 C Foot MRI Brai Chest BC DC DW SVD Figure 4. Compressio Ratio Kee JGRCS 0, All Rights Reserved 49
From the compressio results, it could be oted both DW ad SVD perform well o medical images. While comparig DW ad SVD, SVD raks first with efficiecy gai of more tha.%. BC s performace is very poor i compariso. F. PSNR Figure 5 shows the PSNR values obtaied for the differet techiques selected o the test images. Compressio Ratio (%) 50 45 40 35 30 5 0 5 5 0 C Foot MRI Brai Chest BC DC DW SVD Figure 5. PSNR Agai from the results, it could be see that both DW ad SVD s ability of producig quality decompressed image is more whe compared to BC ad DCR. However, o average, the performace of wavelet with respect to decompressed image quality is better tha SVD. G. Compressio ad Decompressio ime he compressio ad decompressio time take by the four selected algorithms is show i able I. ABLE I. Kee COMPRESSION AND DECOMPRESSION IME Image C D C D C D C D C 0. 0.4 0.4 0.3 0.3 0.6 0. 0. Foot 0.6 0. 0.3 0.5 0.3 0.5 0. 0. MRI 0.9 0.9 0.3 0.7 0.6 0.09 0.3 0.3 Brai 0.3 0.6 0.3 0.4 0.4 0.6 0. 0.5 Chest 0.33 0.8 0.34 0.5 0.6 0.4 0.9 0.09 Kee 0.8 0.3 0.6 0. 0. 0.9 0.8 0.08 Agai from the results, it could be see that the performace of DW ad SVD are o par with each other. O average, SVD is quicker tha DW. BC seems to be the slowest of all the four algorithms. CONCLUSION his paper aalyzed the applicability of four lossy image compressio techiques, amely, BC, DC, DW ad SVD. From the results, it could be cocluded that both DW ad SVD ca be applied safely to compress medical images. DW, achieves better compressio ratio, but falls behid SVD i terms of PSNR ad time. Sice, image quality is give more importace i medical domai, from the preset study, it could be cocluded to select SVD as the right choice for medical image compressio followed by DW. BC ad DC may be adopted by medical applicatios like telecoferecig, where the quality is ot give much importace. I future, hybrid techiques which combie DW ad SVD could be desiged ad tested. REFERENCES [] Norce, R., Podesser, M., Pommer, A., Schmidt, H.P. ad Uhl, A. (003) Cofidetial storage ad trasmissio of medical image data, Computers i Biology ad Medicie, Vol. 33, Pp.77 9. [] Loussert, A., Alfalou, A., El Sawda, R. ad Alkholidi, A. (008) Ehaced System for image's compressio ad ecryptio by additio of biometric characteristics, Iteratioal Joural of Software Egieerig ad its Applicatios, Vol., No., Pp. -8. [3] Peebaker, W.B. ad Mitchell, J.L. (993) JPEG: Still Image Data Compressio Stadard, New York: Va Nostrad Reihold, New York, NY. [4] aubma, D. ad Marcelli, M. (00) JPEG000: Image Compressio Fudametals, Practice ad Stadards, Kluwer Academic Publishers. [5] Mallat, S. (999) A Wavelet our of Sigal Processig, d Editio, Academic Press, Sa Diego. [6] Karras, D.A. (009) Compressio of MRI images usig the discrete wavelet trasform ad improved parameter free Bayesia restoratio techiques, IEEE Iteratioal Workshop o Imagig Systems ad echiques, 009. IS '09, Pp. 73-76. [7] Che, C.W., Zhag, Y.Q. ad Parker, K.J. (994) Subbad aalysis ad sythesis of columetric medical images usig wavelet, Visual Commuicatio ad Image Processig 94, Vol. 306, No. 3, Pp.544 555. [8] Che, C.W., Zhag, Y.Q., Luo, J. ad Parker, K.J. (995) Medical image compressio with structure-preservig adaptive quatizatio, Visual Commuicatio ad Image Processig 95, Vol. 50, No., Pp.983 994. [9] Storm, J. ad Cosma, P.C. (997) Medical image compressio with lossless regios of iterest, Sigal Processig, Vol. 59, No., Pp.55 7. JGRCS 0, All Rights Reserved 50