A Research Paper On Reducion Of Speckle Noise In Ultrasound Imaging Using Wavelet And Contourlet Transform

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1 A Research Paper On Reducon Of Speckle Nose In Ultrasound Imagng Usng Wavelet And Contourlet Transform MR. HITESH S. ASARI, ASS.PROF. AMI SHAH M.E.[Sgnal Processng And Communcaton] Student, Department Of Electroncs and Communcaton, A.D. Patel nsttute and Technologey, New Vallabh Vdhyanagar, Anand Asst.Professor, Department Of Electroncs and Communcaton, A.D. Patel nsttute and Technologey, New Vallabh Vdhyanagar, Anand Abstract Ultrasound s a medcal magng technque that s wdely used for dagnostc purposes. Ultrasound s used for x-ray and ultrasonography. A major problem regardng these mages s n ther nherent corrupton by speckle nose. The presence of speckle noses severely hampers and the nterpretaton and analyss of medcal ultrasound mages. There are many algorthms are proposed for reducng the mxer of nose n medcal ultrasound mages. In ths paper, speckle nose removed s done by methods based on wavelet transform and counterlet transform. The two proposed alternatve methods are evaluated and compared n terms of flter assessment parameters namely peak Sgnal to Nose Rato (PSNR), Sgnal to Nose Rato (SNR), Mean Square Error (MSE), Varance and Correlaton Coeffcent(CC). At last ths method compare wavelet and counterlet transforms and see whch better transform s. Keywords -speckle nose,contourlet transform, logarthmc thresholdng, ultrasonc mages, wavelet transform. I. INTRODUCTION Ultrasound or ultrasonography s a medcal magng technque that uses hgh frequency sound waves and ther echoes, Known as a pulse echo technque. The technque s smlar to the echolocaton used by bats, whales and dolphns, as well as SONAR used by submarnes etc. Medcal magng s an mportant source of dagnosng the malfunctons nsde human body. Some crucal Medcal magng nstruments are X-ray, Ultrasound, Computed Tomography (CT), and Magnetc Resonance Imagng (MRI). Medcal ultrasound magng s one of the sgnfcant technques n detectng and vsualzng the hdden body parts. There could be dstortons due to mproper contact or ar gap between the transducer probe and the human body. Another knd of dstorton that may occur durng ultrasound magng s due to the beam formng process and also durng the sgnal processng stage. In order to overcome through varous dstortons, mage processng has been successfully used. Image processng s a sgnfcant technque n medcal feld, especally n surgcal decsons. Convertng an mage nto homogeneous regons has been an area of hot research from a decade, especally when the mage s made up of complex textures. Varous technques have been proposed for ths task, ncludng spatal frequency technques. Image processng technques have been used wdely dependng on the specfc applcaton and mage modaltes. Computer based detecton of abnormal growth of tssues n a human body are preferred to manual processng methods n the medcal nvestgatons because of accuracy and satsfactory results. Several methods for processng the ultrasound mages have been developed. A major problem regardng these mages s n ther nherent corrupton by speckle nose. The presence of speckle nose severely hampers the nterpretaton and analyss of medcal ultrasound m ages. The objectve of the report s to propose a method for removal of nose n the medcal ultrasound mages. The mage nose content s assumed to be the mxture of speckle and Gaussan nose. Two alternatve algorthms are proposed for reducng the mxed nose n medcal ultrasound mages. Whle speckle nose removal s done by method based on wavelet transform (WT), Laplacan pyramd transform (LP) or contourlet transform (CT), the Gaussan nose component s reduced by Gaussan flter ether n the preprocessng or post processng stage. The two proposed alternatve methods are evaluated n terms of flter assessment parameters namely Peak Sgnal to Nose Rato (PSNR), Sgnal to Nose Rato (SNR), Mean Square Error (MSE), Varance and Correlaton Coeffcent (CC). The expermental results show that Gaussan flter n preprocessng stage s found to be effectve n despecklng based on Laplacan pyramd transform and contourlet transform.[] ISSN: NOV TO OCT 3 VOLUME 0, ISSUE - 0 Page 800

2 II. WAVELET TRANSFORM Wavelets convert the mage nto a seres of wavelets that can be stored more effcently than pxel blocks. Although wavelets also have rough edges, they are able to render pctures better by elmnatng the blockness that s a common feature of DCT based compresson. Not only does ths make for smoother color tonng and clearer edges where there are sharp changes of color, t also gves smaller fle szes than a JPEG mage wth the same level of compresson. A. One-Dmensonal Dscrete Wavelet Transform Two man methods exst for the mplementaton of D-DWT:. The tradtonal convoluton-base the mplementaton. The lftng-based mplementaton B. Two-The -D Dscrete Wavelet Transform The -D DWT operates n a straghtforward manner by nsertng array transposton between the two -D DWT. Dmensonal Dscrete Wavelet Transform. The rows of the array are processed frst wth only one level of decomposton. Ths essentally dvdes the array nto two vertcal halves, wth. The frst half storng the average coeffcents,. Whle the second vertcal half stores the detal coeffcents. Ths process s repeated agan wth the columns, resultng n four sub-bands. The result s shown n Fgure and s decomposed nto four quadrants wth dfferent nterpretatons. Human vsual system s very much senstve to low frequency and hence, the decompose data avalable n the lower sub-band regon and s selected and transmtted, nformaton n the hgher sub-bands regons are rejected dependng upon requred nformaton content. LL: The upper left quadrant conssts of all coeffcents, whch were fltered by the analyss low pass flter ĥ along the rows and then fltered along the correspondng columns wth the analyss low pass flter ĥ agan. Ths sub block s denoted by LL and represents the approxmated verson of the orgnal at half the resoluton. HL/LH: The lower left and the upper rght blocks were fltered along the rows and columns wth ĥ and ĝ, alternatvely. The LH block contans vertcal edges, mostly. In contrast, the HL block shows horzontal edges very clearly. HH: The lower rght quadrant was derved analogously to the upper left quadrant but wth the use of the analyss hgh pass flter ĝ whch belongs to the gven wavelet. We can nterpret ths block as the area, where we fnd edges of the orgnal mage n dagonal drecton. The two dmensonal wavelet transform can be appled to the coarser verson at half the resoluton, recursvely, n order to further decorrelate neghborng pxels of the nput mage. So the mage can be shown as below[3]. Fg. one dmensonal CDF (,) wavelet transform appled to the rows of the benchmark mage lena wth reflecton at the mage boundares[3] Snce we have restrcted the mages to be of quadratc l sze N for Ɩ ϵ N, we can perform at most l log N levels of transform. Thereafter the coeffcent n the upper left corner represents the average grey scale value of the whole mage and s called DC coeffcent (DC : drect current). In practce, usually four up to sx level of wavelet transform level wll be performed. (a) Two levels (b) Three levels (c) Four levels D-DWT Fg. Mult resoluton scheme after several levels of wavelet transform[3] III. CONTOURLET TRANSFORM Image processng typcally reles on smple statstcal models to characterze mages. Natural mages tend to have certan common characterstcs that make them look natural. The major drawback for wavelets n two-dmensons s ther lmted ablty n capturng drectonal nformaton. To overcome ths defcency, researchers have recently consdered multscale and drectonal representatons that can capture the ntrnsc geometrcal structures such as smooth contours n natural mages. In partcular, the curvelet transform, poneered by Cand`es and Donoho, was shown to be optmal n a certan sense for functons n the contnuous doman wth curved sngulartes. Inspred by curvelets, Do[7] and Vetterl[7], developed the contourlet transform based on an effcent two-dmensonal multscale and drectonal flter bank that can deal effectvely wth mages havng smooth contours. Contourlets not only possess the man features of wavelets (namely, multscale and tme-frequency localzaton), but also offer a hgh degree of drectonalty and ansotropy.[4] ISSN: NOV TO OCT 3 VOLUME 0, ISSUE - 0 Page 80

3 Fg. 3 Contourlet Transform [5] The Laplacan Pyramd at each level generates a Lowpass output (LL) and a Band pass output (LH, HL, and HH). The Band pass output s then passed nto Drectonal Flter Bank, whch results n contourlet coeffcents. The Low pass output s agan passed through the Laplacan Pyramd to obtan more coeffcents and ths s done tll the fne detals of the mage are obtaned.[5]. Contourlets were developed as an mprovement over wavelets n terms of ths neffcency. The resultng transform has the multscale and tme-frequencylocalzaton propertes of wavelets, but also offers a hgh degree of drectonalty and ansotropy. Specfcally, contourlet transform nvolves bass functons that are orented at any power of two s number of drectons wth flexble aspect ratos. Wth such a rch set of basc functons, contourlets can represent a smooth contour wth fewer coeffcents compared wth wavelets Fg. 4 Drectonal Flter Bank [6] The Nonsubsampled Pyramd (NSP): What gves the mult-scale property of the NSCT s a shft-nvarant flterng structure that acheves a subband decomposton smlar to that of the Laplacan pyramd. Our soluton s obtaned by usng twochannel nonsubsampled -D flter banks. Fgure 4 llustrates the proposed nonsubsampled pyramd (NSP) decomposton wth J 3 stages. Such expanson s conceptually smlar to the -D nonsubsampled wavelet transform computed wth the J + redundancy, where J denotes the number of decomposton stages. The deal passband support of the low pass flter at the j-th stage s the regon, π π j j. Accordngly, the deal support of the equvalent hghpass flter s the complement of the lowpass,.e., the regon, /, π π π π j j j j The flters for subsequent stages are obtaned by upsamplng the flters of the frst stage. Ths gves the mult-scale property wthout the need for addtonal flter desgn. The proposed structure s thus dfferent from the separable nonsubsampled wavelet transform (NSWT). In partcular, one bandpass mage sproduced at each stage resultng n J + redundancy. By contrast, the separable NSWT produces three drectonal mages at each stage resultng n 3J + redundancy. The proposed pyramd s not the only -D pyramd wth redundancy. The -D pyramd proposed n s obtaned wth a smlar structure. Specfcally, the NSFB of s bult from a gven low pass flter H 0 ( z). One then sets H ( z ) H 0 ( z ), and G ( z ) G 0 ( z ). Ths perfect reconstructon system can be seen as a partcular case of our more general structure. The advantage of our constructon s that t s less restrctve and as a result, better flters can be obtaned[6] IV Algorthms for removng speckle nose: To be able to derve an effcent despeckle flter. a speckle nose model s needed. The speckle nose model for ultrasound mages may be approxmated as multplcatve. The sgnal at the output of the ultrasound magng system may be defned as[3] g(,j) f(,j)u(,j) + n(,j) () where, g(,j) the nosy pxel n the mage; f(,j) nose free pxel; u(,j) multplcatve nose; n(,j) addtve nose;,j are the ndces of the spatal locatons that belong to the D space of real numbers,, j. The speckle nose becomes very close to the whte Gaussan nose correspondng to the uncompressed Raylegh sgnal. In partcular, t should be noted that speckle s no longer multplcatve n the sense that, on homogenous regons, g(, j )can be assumed to be constant, the mean s propostonal to varance rather than standard devaton. In the Eq., the effect of the addtve nose s consderably smaller compared wth that of the multplcatve nose and, hence, t may be wrtten as g(, j ) f (, j ) + u(, j ) () The logarthmc operaton transforms the model n the Eq. nto the classcal sgnal n the addtve nose form as ISSN: NOV TO OCT 3 VOLUME 0, ISSUE - 0 Page 80

4 log (g(, j )) log (f (, j )) + log (u(, j )) (3) Thus the problem of despecklng s reduced to the problem of rejectng an addtve nose, and a varety of nose suppresson technques could be evoked n order to perform the task A. For wavelet transform Step : Input medcal ultrasound mage X. Step : Apply log transformaton to the nput mage X. Step 3: Apply the wavelet transform on the log transformed mage of the Step upto n levels of subband decomposton at each level. Step 4: Perform thresholdng of the transformed mage of the Step 3. Step 5: By performng the nverse transform on the thresholded mage of the Step 4, the despeckled mage Y s obtaned (output mage). Step 6: Compute the values of the performance parameters, namely, varance, MSE, SNR,PSNR, correlaton coeffcent for the despeckled mage Y of the Step 5. B. For contourlet transform Step : Input medcal ultrasound mage X. Step : Apply log transformaton to the nput mage X. Step 3: Apply the contourlet transform on the log transformed mage of Step upto n levels of Laplacan pyramdal decomposton and m drectonal decompostons at each level. Step 4: Perform thresholdng of contourlet transformed mage of Step 3. Step 5: By performng the nverse contourlet transform on the threshold mage of Step 4, the despeckled mage Y s obtaned (output mage). Step 6: Compute the performance parameters, namely, varance, MSE, SNR, PSNR, correlaton coeffcent for the despeckled mage Y of Step 5. In the Step 4, the wavelet or contourlet transformed mage can be threshold by : I. Selectng ether global or subband thresholdng functon, II. Selectng shrnkage scheme (Hard, Soft or Sem-soft), III. Selectng Bayes shrnkage or unversal shrnkage rule.[4] ADAPTIVE THRESHOLDING It s mportant to know about the three categores of thresholdng. They are hard thresholdng, soft thresholdng and sem-soft thresholdng. In hard thresholdng all coeffcents whose magntude s greater than the selected threshold value λ remans same and the others whose magntude s smaller than λ are set to zero. In soft thresholdng, the coeffcents whose magntude s greater than the selected threshold value are shrunk towards zero by an amount of threshold λ and others set to zero. The am of semsoft thresholdng s to offer a compromse between hard and soft thresholdng by changng the gradent of the slope. we defne the followng thresholdng functons: Hard thresholdng: (4) Soft thresholdng (5) Sem-soft thresoldng (6) Shrnkage rule Bayes shrnk has been proposed by Chang, Yu and Vetterl. The goal of ths method s to mnmze the Bayesan rsk, and hence ts name Bayes shrnks. It s a subband dependent method where threshold level s selected at each subband of resoluton n the contourlet decomposton. The Bayes threshold on a gven subband s, wth zero mean varable X, s gven by λs n x (7) where, the estmated nose varance found as the medan of the absolute devaton of the contourlet coeffcents on the fnest level L, s gven by n medan ({ x, j L}) (8) The value s the medan absolute devaton of normal dstrbuton wth zero mean and unt varance. The estmated sgnal varance on the sub band consdered, s gven by x y max( y n,0 ) (9) an estmate of the varance of the observatons, N S y W N k s gven s (0) Where N s number of the counterlet coeffcent k k W subband consderaton FILTER ASSESSMENT: The qualty of an mage s examned by objectve evaluaton as well as subjectve evaluaton. ISSN: NOV TO OCT 3 VOLUME 0, ISSUE - 0 Page 803

5 For subjectve evaluaton, the mage has to be observed by a human expert. But the Human Vsual System (HVS) s so complcated and ths cannot gve the exact qualty of mage. The followng metrcs are used for objectve evaluaton of the orgnal mage X and the despeckled mage Y.. Nose varance : It determnes the contents of the speckle n the mage. N N j 0 (). Mean Square Error (MSE) : The MSE measures the qualty change between the orgnal mage (X) and denosed mage (Y) and s gven by N MSE ( Y j X j ) N j 0 () 3. Sgnal-to-Nose Rato (SNR) : The SNR compares the level of desred sgnal to the level of background nose. The hgher the rato, the less obtrusve the background nose s. It s expressed n decbels (db) as g SNR 0 log 0 ( ) e (3) Where g Dfference between the orgnal and denosed mage. 4. Peak Sgnal-to-Nose Rato (PSNR): The PSNR s computed as PSNR 0 log 0 x s ( MSE (4) Where, S s the maxmum ntensty n the orgnal mage. The PSNR s hgher for a better-transformed mage and lower for a poorly transformed mage. It measures mage fdelty, that s, how closely the transformed mage resembles the orgnal mage. 5. Correlaton Coeffcent (CC): It represents the strength and drecton of a lnear relatonshp between two varants. The best known s the Pearson product moment correlaton coeffcent, whch s obtaned by dvdng the covarance of the two varables by the product of ther standard devaton, as gven by CC N X j N X Y X Y ( X) N Y ( Y (5) If the correlaton coeffcent s near to +, then there exsts stronger postve correlaton between the orgnal and despeckled mage.[4] ) ) (a)orgnal Image (C)Denose usng Wavelets V RESULTS (b)nosy Image (d)denose usng Contourlets Fg.5 (a) orgnal mage (b) nosy mage wth varance 0.7 (c) Wavelet denosng (d) contourlet denosng wth logarthmc threshold TABLE I. COMPARISION RESULTS BETWEEN WAVELET TRANSFORM AND CONTOURLET TRANSFORMS WITH LOGARITHMIC THRESHOLD, FOR A ABOVE IMAGE. Noce Wavelet Transform varanc e MS SNR PSN E R Contourlet transform MS SNR PSN E R CONCLUSION Wavelets transform and contourlets transform makes sharp boundary of natural mage. So they are used for the remove speckle nose n ultrasound mage. They are used for compresson and make boundary sharp so everyone can detect the boundary of mage. As shown n fgure 5 and results of SNR n table contourlet transform has more SNR than wavelet so contourlet s better than wavelet. REFERENCES [] Performance Comparson of Wavelet Transform and Contourlet Transform based methods for Despecklng Medcal Ultrasound Images by P.S. Hremath, Prema T. Akkasalgar, and Sharan Badger. Internatonal ISSN: NOV TO OCT 3 VOLUME 0, ISSUE - 0 Page 804

6 Journal of Computer Applcatons ( ) Volume 6 No.9, July 0 [] Implementaton of Dscrete Wavelet Transform Processor For Image Compresson Processor For Image Compresson by Ms.Yamn S.Bute, Prof. R.W. Jasutkar nternatonal Journal of Computer Scence and Network (IJCSN),Volume, Issue 3, June 0 [3] wavelet transforms on mage, thess report, unpublshed. [4] Drectonal Multscale Modelng of Images usng the Contourlet Transform by Duncan D.-Y. Po and Mnh N. Do, Member, IEEE. [5] Medcal Image Denosng Usng Adaptve Threshold Based On Contourlet Transform S.Satheesh, Dr.KVSVR Prasad. Advanced Computng: An Internatonal Journal ( ACIJ), Vol., No., March 0 [6] Mnh N. Do, Member, IEEE, and Martn Vetterl, Fellow, IEEE,The Contourlet Transform: An Effcent Drectonal Multresoluton Image Representaton. IEEE TRANSACTIONS ON IMAGE PROCESSING [7] Speckle Reducng Contourlet Transform for Medcal Ultrasound Images by P.S. Hremath, Prema T. Akkasalgar and Sharan Badger, Internatonal Journal of Computer and Informaton Engneerng 4:4 00 [8] Mersad Mrzavand, Mehran Yazd, : A Logarthmc Threshold Contourlet Based Method for Speckle Nose Reducton Of Medcal Ultrasound Images,Canadan Journal on Image Processng and Computer Vson Vol. 3 No., March 0. [9] The Nonsubsampled Contourlet Transform: Theory, Desgn, and Applcatons,IEEE Arthur L. Cunha, Student Member, IEEE, Janpng Zhou, Student Member, IEEE, and Mnh N. Do, Member, IEEE. IEEE TRANSACTIONS ON IMAGE PROCESSING, MAY 0 [0] Implementaton of Dscrete Wavelet Transform Processor For Image Compresson Processor For Image Compresson by Ms.Yamn S.Bute, Prof. R.W. Jasutkar Dept of CSE,,G.H. Rason College of Engg Nagpur Dept CSE G.H. Rason College of, Engg Nagpur. Internatonal Journal of Computer Applcatons ( ) Volume, June 0 []. A New Contourlet Transform Wth Sharp Frequency Localzaton unplshed, Yue Lu and Mnh N. Do, [] Performance Comparson of Wavelet Transform and Contourlet Transform based methods for Despecklng Medcal Ultrasound Images, by P.S. Hremath, Prema T. Akkasalgar, and Sharan Badger. Internatonal journal of computer scence. July 0. [3] Speckle Nose Reducton of Medcal Ultrasound Images usng Bayesshrnk Wavelet Threshold by K. Karthkeyan and Dr. C. Chandrasekar, Internatonal Journal of Computer Applcatons, May 0. [4] Speckle Nose Reducton n Ultrasound Images by Wavelet Thresholdng by Ms. Alka Vshwa and Ms. Shlpa Sharma, February 0. [5] Wavelet Transform In Image Recognton by Aleˇs Proch azka, Andrea Gavlasov a, and Karel Volka, IEEE. [6] contourlet by M. N. Do and M. Vetterl. IEEE. ISSN: NOV TO OCT 3 VOLUME 0, ISSUE - 0 Page 805