Wavelet Based Dual Encoding Lossless Medical Image Compression

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1 avelet Based Dual Ecodig Lossless Medical Image Compressio *V.Maohar, Asst. Professor, SR Egieerig College, aragal, TG, Idia, **Dr.G. Laxmiarayaa, Professor, oly Mary Istitute of Techology, yderabad, TG, Idia, ABSTRACT Medical image compressio usig dual ecodig scheme which helps i lossless image compressio ad wavelet helps i icreasig the sparsity of the image. Dual ecodig scheme comprised with Ru legth Codig ad 8X8 Bad ecodig schemes, these will icrease the affiity of the image ad reduces the redudacy of pixels i image. To authorize this ovel ecodig scheme uffma table created for calculatig average legth ad etropy of the image by Terary uffma code or o-biary uffma code. Fially PSNR, MSE, Block compressio, Total compressio ad Etropy were calculated ad tabulated. KEY ORDS: Medical Image, Compressio, ru legth ecodig, uffma codig, 8X8 block codig. 1. INTRODUCTION I Picture squeezig codig is will store those picture uder bit-stream as coservative Likewise coceivable ad with show the decoded picture i the scree as accurate as time permits. At the ecoder receives the first picture file, the picture documet will a chace to be chaged over uder a arragemet of double data, which will be kow as those bit-stream. Those decoder after that receives the ecoded bit-stream ad decodes it to structure the decoded picture. O the dowright iformatio amout of the bit-stream will be short of what those aggregate iformatio amout of the first image, At that poit this will be called picture squeezig. Those layerig proportio will be characterized as takes after: 1 Cr, (1) where 1 is those iformatio rate of first picture hat's more is that of the ecoded bit-stream. Etire ecodig buildig desig of picture squeezig framework may be idicated will be figure 1. The essetial priciple ad idea of every utilitaria square will a chace to be preseted i the Emulatig segmets. 1.1 Reduce the Correlatio betwee Pixels The reaso is that the correlatio betwee oe pixel ad its eighbor pixels is very high, or we ca say that the values of oe pixel ad its adjacet pixels are very similar. Oce the correlatio betwee the pixels is reduced, we ca take advatage of the statistical characteristics ad the variable legth codig theory to reduce the storage quatity. This is the most importat part of the image compressio algorithm; there are a lot of relevat processig methods beig proposed. The bestkow methods are as follows: Figure1. The geeral ecodig flow of image compressio result i some loss of details ad urecoverable distortio. Subbad Codig: Subbad Codig such as Discrete avelet Trasform (DT) is also a lossy codig method. The objective of subbad codig is to divide the spectrum of oe image ito the lowpass ad the highpass compoets. JPEG 000 is a -dimesio DT based image compressio stadard. Predictive Codig: Predictive Codig such as DPCM (Differetial Pulse Code Modulatio) is a lossless codig method, which meas that the decoded image ad the origial image have the same value for every correspodig elemet. Orthogoal Trasform: Karhue-Loeve Trasform (KLT) ad Discrete Cosie Trasform (DCT) are the two most well - kow orthogoal trasforms. The DCTbased image compressio stadard such as JPEG is a lossy codig method that will 1. Quatizatio The objective of quatizatio is to reduce the precisio ad to achieve higher compressio ratio. For istace, the origial image uses 8 bits to store oe elemet for every pixel; if we use less bits such as 6 bits to save the iformatio of the image, the the storage quatity will be reduced, ad the image ca be compressed. The shortcomig of quatizatio is that it is a lossy operatio, which will result ito loss of precisio ad urecoverable distortio. 1.3 Etropy Codig The mai objective of etropy codig is to achieve less average legth of the image. Etropy codig assigs codewords to the correspodig symbols accordig to the Page 1180

2 probability of the symbols. I geeral, the etropy ecoders are used to compress the data by replacig symbols represeted by equal-legth codes with the codewords whose legth is iverse proportioal to correspodig probability..1 BLOCK DIAGRAM. PROPOSING SCEME I/P Image avelet Decompositio NBZ COMPRESSION OF AN IMAGE *DT uffma Codig Ru legth Codig Quatizatio RECONSTRUCTION OF A COMPRESSED IMAGE Compressed Image Data Decodig & De- Quatizatio Iverse avelet Trasform Recostructed Image. ORK FLO Step 1: Iput a -D image A. Step : Obtaiig Pre-processig Stage o iput image A. Step 3: Apply wavelet decompositio of the image [ere the decompositio is depeds o the umber of levels for a iput this may vary from 1 to 7 Discrete avelet Trasformatios ad output is C]. Step 4: Zero DT is apply by usig a threshold output levels. Step 5: For Row is equal to oe dow to Legth of last level decomposed image. Step 6: If C < Threshold value, the Step 7: C = 0 & The Number of zeros will be icreased. Step 8: ed Step 9: ed Step 10: Quatizatio matrix will be calculated ad applied o to the image. Quatizatio(CQ)= ( 1 + )*(C-DT ) / (DT DT ) here: Q is the Block size DT is the miimum value of C DT is the maximum value of C Step 11: Apply Ru legth ecodig scheme. Step 1: Apply uffma ecodig scheme. Step 13: Ru legth codig output Legth of data is L 1. If L<4 the. If L~0 the 3. Lc = Lc+1 4. Ed 5. Ed Figure : Block Diagram of D Lossless Compressio. Step 14: Fially the image values were stored with *DT scheme..3 AVELET D TRANSFORM I subbad codig, the spectrum of the iput is decomposed ito a set of bad limited compoets, which is called sub bads. Ideally, the sub bads ca be assembled back to recostruct the origial spectrum without ay error. Figure 3 shows the block diagram of two-bad filter bak ad the decomposed spectrum. At first, the iput sigal will be filtered ito low pass ad high pass compoets through aalysis filters. After filterig, the data amout of the low pass ad high pass compoets will become twice that of the origial sigal; therefore, the low pass ad high pass compoets must be dow sampled to reduce the data quatity. At the receiver, the received data must be upsampled to approximate the origial sigal. Fially, the upsampled sigal passes the sythesis filters ad is added to form the recostructed approximatio sigal. After subbad codig, the amout of data does ot reduce i reality. owever, the huma perceptio system has differet sesitivity to differet frequecy bad. For example, the huma eyes are less sesitive to high frequecy-bad color compoets, while the huma ears is less sesitive to the low-frequecy bad less tha 0.01 z ad high-frequecy bad larger tha 0 Kz. e ca take advatage of such characteristics to reduce the amout of data. Oce the less sesitive compoets are reduced, we ca achieve the objective of data compressio. Page 1181

3 () () 0 1 Figure 3 Two-bad filter bak for oe-dimesio subbad codig ad decodig where measures variatios alog colums (like Now back to the discussio o the DT. I two V dimesioal wavelet trasform, a two-dimesioal horizotal edges), respods to variatios alog rows scalig fuctio, ( x,) y, ad three two-dimesioal D (like vertical edges), ad correspods to variatios wavelet fuctio ( x,) y, V ( x,) y ad D ( x,) y alog diagoals., are required. Each is the product of a oe-dimesioal Similar to the oe-dimesioal discrete wavelet scalig fuctio (x) ad correspodig wavelet fuctio trasform, the two-dimesioal DT ca be (x). implemeted usig digital filters ad samplers. ith ( x,)()() y x y ( x,)()() y x y separable two-dimesioal scalig ad wavelet fuctios, we simply take the oe-dimesioal DT of the rows of V ( x,)()() y y x D ( x,)()() y x y () f (x, y), followed by the oe-dimesioal DT of the resultig colums. Figure 4 shows the block diagram of two-dimesioal DT. ( j 1, m,) h () h () m h () m D V h () h () m h () m Figure4. D avelet Decompositio.3.1 D-AVELET MALICIOUS TREE DECOMPOSITION The followig sub-bad decompositio of ad image ca be give as X(m,, ) = X (m) X (m) X () X () (3) here X (m, ) is two dimesioal image ad is subbad decompositio is observed i the equatio, subscripts j, k are stads for temporal directio. From the above equatio we ca fid 8 sub-bads. X (m, ) G G G Page 118

4 Figure5. D avelet Decompositio.4 QUANTIZATION To reduce the umber of bits eeded to represet the trasform coefficiets, the coefficiet a b (u,v) of subbad b is quatized to value q b (u,v) usig (4) q (, ) ( 1 + ) where the quatizatio step size is (, ) (, ) (4) R b b b b 1 11 (5) Rb is the omial dyamic rage of subbad b, adε b adμ b are the umber of bits allotted to the expoet ad matissa of the subbad s coefficiets, respectively. The omial dyamic rage of subbad b is the sum of the umber of bits used to represet the origial image ad the aalysis gai bits for subbad b. Quatizatio operatio is defied by the step size Δb, the selectio of the step size is quite flexible, but there are a few restrictios imposed by the JPEG 000 stadard. 1. Reversible wavelets: whe reversible wavelets are utilized i JPEG 000, uiform dead zoe scalar quatizatio with a step size of Δb =1 must be used.. Irreversible wavelets: whe irreversible wavelets are utilized i JPEG 000, the step size selectio is restricted oly by the sigallig sytax itself. The step size is specified i terms of a expoet ε b, 0 ε b < 5, ad a matissa μ b, 0 μ b < RUN LENGT ENCODING Ru legth ecodig (RLE) is a simple techique to compress digital data by represetig successive rus of the same value i the data as the value followed by the cout, rather tha the origial ru of values. The goal is to reduce the amout of data eeded to be stored or trasmitted. The eed to use ru legth ecodig ofte arises i various applicatios i DSP, especially image processig ad compressio. Example of RLE: Origial RLE Represetatio As we ca see from the above simple example, RLE works the best whe applied to data where there are successive rus of the same values. Although oe might thik that such situatios are trivial ad ot the orm, they actually appear over ad over i may fields of DSP. As a example, whe applyig a low-frequecy digital filter agaist a radom iput of varyig frequecies, all the frequecies above the cut-off frequecy will be represeted as 0. Thus i the correspodig output, there would be rus of 0 s which could be better represeted as the value (0) followed by the cout of cosecutive 0 s. Aother real world applicatio of RLE is i image processig. Durig image compressio, higher spatial frequecies are filtered out. I the best case, RLE ca reduce data to merely two umbers if all the values i the origial data are exactly the same, regardless of the size of the iput. owever, i the worst case, that is if there are o repeatig values i the data, RLE could actually double the amout of umbers compared with the origial data. Thus RLE should oly be used i cases where rus of the same value are expected. Aother advatage of RLE is a lossless (or reversible) compressio techique. That is ulike some other compressio techiques, such as JPEG, oe ca obtai exactly the origial data. This is doe through a RLE decoder which we have also implemeted i both Mat lab ad assembly code. Figure 6: Curret codig bits ad their eighbours for RLC operatio.6 UFMANN CODING The idea behid uffma codig is to fid a way to compress the storage of data usig variable legth codes. Our stadard model of storig data uses fixed legth codes. For example, each character i a text file is stored usig 8 bits. There are certai advatages to this system. he readig a file, we kow to ALAYS read 8 bits at a time to read a sigle character. Figure 7: uffma Ecodig table. Page 1183

5 I order to evaluate the performace of the image origial image, ad f (x,y)is the pixel value of the compressio codig, it is ecessary to defie a decoded image. Most image compressio systems are measuremet that ca estimate the differece betwee the desiged to miimize the MSE ad maximize the PSNR. origial image ad the decoded image. Two commo used measuremets are the Mea Square Error (MSE) ad the Peak Sigal to Noise Ratio (PSNR), which are defied i (6) respectively. f(x,y) is the pixel value of the PSNR = 0 log10(mse/ max(x)) ( ) 3. RESULTS Parameter Compariso Of Differet avelets aar Daubechies Symlets Coieflets Biorthogoal % Descriptor Coefficiets Block Compressio Total Compressio Etropy PSNR a. b. c. d. e. f. Figure 8: a) Origial Image, Compressed ad Recostructed Images b) aar, c) Daubechies, d) Symlets, e) Coieflets, f) Biorthogoal. The above metioed images i the figure were origial image ad compressed images of various wavelets these are aar, Daubechies, Symlets, Coieflets ad Biorthogoal wavelets ad extracted five metrics from compressed data ad Page 1184

6 recostructed compressed image are the parameters of % Descriptor Coefficiets, Block Compressio, Total Compressio, Etropy ad PSNR. By usig above metioed five parameters ad the results of the simulated images represets Biorthogoal wavelets are much more efficiet the compared to all other wavelets. 4. CONCLUSION A ew image compressio scheme based o discrete wavelet trasform is proposed i this research which provides sufficiet high compressio ratios with o appreciable degradatio of image quality. The effectiveess ad robustess of this approach has bee justified usig a set of real images. From the experimetal results it is evidet that, the proposed compressio techique gives better performace compared to other traditioal techiques. avelets are better suited to time-limited data ad wavelet based compressio techique maitais better image quality by reducig errors. The future directio of this research is to implemet a compressio techique o 3D images. [11] M. Sifuzzama & M.R. Islam1 ad M.Z. Ali, Applicatio of avelet Trasform ad its Advatages Compared to Fourier Trasform Joural of Physical Scieces, Vol. 13, 009, [1] F. Sheg, A. Bilgi, P. J. Semetilli, ad M.. Marcelli, Lossy ad lossless image compressio usig reversible iteger wavelet trasforms, Image Processig, ICIP 98. Proceedigs Iteratioal Coferece o, vol.3, o.4-7, pp , Oct [13] Madhuri A. Joshi, Digital Image Processig, A Algorithmic Approach, PI, New Delhi, pp , 006. REFERENCES [1] R. C. Gozalez ad R. E. oods, "Digital Image Processig", d Ed., Pretice all, 004. [] Liu Chie-Chih, ag sueh-mig, "Acceleratio ad Implemetatio of JPEG 000 Ecoder o TI DSP platform" Image Processig, 007. ICIP 007. IEEE Iteratioal Coferece o, Vo1. 3, pp. III , 005. [3] G. K. allace, "The JPEG Still Picture Compressio Stadard", Commuicatios of the ACM, Vol. 34, Issue 4, pp.30-44, [4] Kamrul asa Talukder ad Koichi arada, "Developmet ad Performace Aalysis of a Adaptive ad Scalable Image Compressio Scheme with avelets", Published i the Proc. of ICICT, March 007, BUET, Dhaka, Bagladesh, pp , ISBN: [5] Rao, K.R., Yip, P., Discrete Cosie Trasform: Algorithms, Advatages, Applicatios. Bosto: Academic Press, [6] Still Image ad video compressio with MATLAB, K. S. Thyagaraja, A JON ILEY & SONS, INC., PUBLICATION. [7] Subramaya, Image Compressio Techique, Potetials IEEE, Vol. 0, Issue 1,pp 19-3, Feb- March 001. [8] Jackso ad aah, Comparative Aalysis of Image Compressio Techiques, System Theory, Proceedigs SSST 93, 5th Southeaster Symposium, pp , 7 9 March [9] Meyer, Y. avelets: their past ad their future, Progress i avelet Aalysis ad its Applicatios. Gif-sur-Yvette, pp 9-18, [10] Rajesh K. Yadav, S.P. Gagwar & arsh V. Sigh, Study ad aalysis of wavelet based image compressio techiques. Iteratioal Joural of Egieerig, Sciece ad Techology,Vol. 4, No. 1, 01, pp Page 1185