Optimum Threshold Parameter Estimation of Wavelet Coefficients Using Fisher Discriminant Analysis for Speckle Noise Reduction

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1 he Internatonal Arab Journal of Informaton echnology, Vol., No. 6, November Optmum hreshold Parameter Estmaton of Wavelet Coeffcents Usng Fsher Dscrmnant Analyss for Speckle Nose Reducton Mohammad Motur Rahman, Mthun Kumar PK and Mohammad Shorf Uddn Department of Computer Scence and Engneerng, MBSU, Bangladesh Department of Computer Scence and Engneerng, Jahangrnagar Unversty, Bangladesh Abstract: Optmzng threshold value of wavelet coeffcent s an mportant task n speckle nose reducton n the wavelet doman. Wthout proper selecton of threshold value mage nformaton may be lost, whch s unwanted. In ths paper we proposed optmum threshold parameter usng Fsher Dscrmnant Analyss (FDA) for determnng the optmum threshold value of wavelet coeffcent for the best speckle nose reducton. It also preserves edges wthout destroyng mage nformaton. he method s compared wth the several other classcal thresholdng methods on varety of mages and the expermental results confrm sgnfcant mprovement over exstng methods. Keywords: FDA, optmum threshold, speckle nose, ultrasound mage, wavelet. Receved July, ; accepted June 4, 3; publshed onlne March 3, 4. Introducton Image denosng s one of the most sgnfcant and fundamental tasks for mage preprocessng. he am of the mage denosng algorthm s to reduce the nose level as well as preservng the mportant mage features or nformaton. Speckle s a partcular knd of multplcatve nose whch occurs n mages obtaned by coherent magng systems lke ultrasound. It tends to degrade the resoluton and contrast of ultrasound mages, thus may lead to elmnate some useful and mportant dagnostc nformaton. In the recent years there has been a far amount of research on wavelet thresholdng for sgnal denosng because wavelet provdes approprate bass for separatng nose sgnal from mage sgnal. he man challenge of ths method s to fnd an optmum threshold value because a small threshold value wll pass all the nosy coeffcents and hence the resultant denosed sgnal may stll be nosy. On the other hand, a large threshold value makes more number of coeffcents as zero whch leads to smooth sgnal and destroys detals and mage may produce blur and artfacts. Many wavelet based thresholdng technques lke hard thresholdng, soft thresholdng, VsuShrnk, SureShrnk, BayesShrnk and Bayes thresholdng [, 3, 4, 5, 6, 7, 8, 9,,, 3, 6] have proved better effcency n mage processng. Bayes thresholdng s selected by maxmum lkelhood estmaton. Fsher Dscrmnant Analyss (FDA) [] has been wdely appled n pattern recognton and classfcaton. For that t s sometme necessary for fndng threshold value. In papers [, 5] FDA s used for selectng optmum threshold value for pattern recognton and classfcaton. In [7] wavelet based denosng preprocessng wth FDA scheme s proposed for fault dagnoss. In ths paper we proposed FDA based thresholdng method for denosng speckle nose of dfferent mages. Fgure shows a smple flow dagram of our system. Speckle Image DW FDA Analyss (Optmal thresholdng) Fgure. Block dagram of the proposed FDA technque for accurate speckle nose reducton and the best edge preservaton approach for ultrasound mage. he paper s organzed as follows: In secton, we defne the ultrasound speckle suppresson problem by outlnng the speckle nose model and the FDA. Secton 3 descrbes wavelet transformaton and wavelet shrnkage. Secton 4 the numercal mplementaton scheme of the proposed FDA optmal threshold method s presented. Secton 5 presents the evaluaton crtera for checkng the flter performance. Secton 6 compares the performance of the proposed method wth other exstng speckle nose reducton methods.. heoretcal Background.. Speckle Nose Model IDW Desre Image Denote by a nosy observaton I(x, y) (.e., the recorded ultrasound mage) of the wo-dmensonal (D) functon f(x,y) (.e., the nose-free mage that has to be recovered) and by η m(x,y) and η a(x,y) the corruptng

2 574 he Internatonal Arab Journal of Informaton echnology, Vol., No. 6, November 4 multplcatve and addtve speckle nose components, respectvely. One can wrte: I(x, y) = f(x, y) η m (x, y) + η a (x, y) () Generally, the effect of the addtve component of the speckle n ultrasound mages s less sgnfcant than the effect of the multplcatve component. hus, gnorng the term η a (x, y), one can rewrte Equaton as: I(x, y) = f(x, y) η m (x, y) () o transform the multplcatve nose model nto an addtve one, we apply the logarthmc functon on both sdes of Equaton... Fsher Dscrmnant Analyss FDA locates drectons effcent for dscrmnaton by yeldng the maxmum rato of between-class scatter to wthn-class scatter. For each mage Fsher Lnear Dscrmnant (FLD) fnds a projecton orentaton of ntensty by whch two classes (object and background) are well separated. For any mage, there s a set X ncludng N ntensty. X = { C, C} = { x, x,, x n } n + n = N Where n and n are cardnalty of subset C and subset C respectvely. If we form a lnear combnaton of the components of x. We obtan: y = w x (4) Of all the possble lnes we would lke to select the one that maxmzes the separablty of the scalars. In order to fnd a good projecton vector, we need to defne a measure of separaton. he mean vector of each class n x space and y space s: And µ = x Îω x N (5) µ ɶ = yîω y = W x =W µ xîω N N We can then choose the dstance between the projected means as our objectve functon: ɶ ɶ (7) J(W) = µ - µ = W (µ - µ ) However, the dstance between projected means s not a good measure snce, t does not account for the standard devaton wthn classes. Fsher suggested maxmzng the dfference between the means, normalzed by a measure of the wthn-class scatter. For each class we defne the scatter, an equvalent of the varance, as: s ɶ = yîω (y - µ ɶ ) (3) (6) (8) Where the quantty ( Sɶ + S ɶ ) s called the wthnclass scatter of the projected examples. he FLD s defned as the lnear functon W x that maxmzes the crteron functon: µ ɶ - µ ɶ J(W ) = S ɶ + Sɶ herefore, we are lookng for a projecton examples from the same class are projected very close to each other and, at the same tme, the projected means are as farther apart as possble. o fnd the optmum W, frst we defne a measure of the scatter n feature space x: s = xîω (x - µ )(x - µ ) () S + S =S W () Where S W s called the wthn class scatter matrx. he scatter of the projecton y can then be expressed as a functon of the scatter matrx n feature space x: s ɶ = yîω (y - µ ɶ ) = xîω (W x -W µ ) = xîω W (x - µ )(x - µ ) W = W S W S + S = W SwW ɶ ɶ (3) Smlarly, the dfference between the projected means can be expressed n terms of the means n the orgnal feature space: ( µ ɶ - µ ɶ ) = (W µ -W µ ) =W ( µ - µ )( µ - µ ) W =W S BW he matrx S B s called the between class scatter. Note that, snce S B s the outer product of two vectors, ts rank s at most one. We can fnally express the fsher crteron n terms of S W and S B as: W S BW J(W ) = W SW W o fnd the maxmum of J(W) we derve and equate to zero: Dvdng by d d W S BW [J(W)] = dw dw W SW W = Þ d W S BW d W S WW W SW W - W S BW = Þ dw dw W SWW S BW - W S BW SW W = W S W W : W SW W W S BW S BW - W SW W W SW W S BW - JSW W = Þ - SW S BW - JW = SW W = Þ Solvng the generalzed egen value problem yelds S S W JW W B = : * W S BW - W = argm ax S W (µ - µ ) W SW W hs s knows as FLD. (9) () (4) (5) (6) (7) (8)

3 Optmum hreshold Parameter Estmaton of Wavelet Coeffcents Usng Fsher Dscrmnant Analyss for Wavelet echnque 3.. Wavelet ransform D scalng and wavelet functons are used for wavelet transformaton. he scaled and translated bass functons are: j / j j f j,m,n (x, y) = f( x - m, y - n) j / j j ψ ju,m,n (x, y) = ψ ( x - m, y - n) Where: ={H,V,D}. he Dscrete Wavelet ransform (DW) of functon f(x, y) of sze M N then: M - N - W f (j, m, n) = f(x, y)f j,m,n (x, y) MN x= y= Where: ={H,V,D}. M - N - W ψ (j, m, n) = f(x, y)ψ j,m,n (x, y) MN x= y= We get four subband coeffcent values from mage for applyng DW. hose subbands are Approxmaton and Detal, Detal ncludes horzontal, vertcal, dagonal. If we want to get the prevous data then have to perform the nverse operaton. he Inverse Dscrete Wavelet ransform (IDW) s: f(x, y) = W f (j, m, n)f j,m,n (x, y) MN m n + W ψ (j, m, n)ψ j,m,n (x, y) MN =H,V,D j= j m n (9) () () () (3) After executon of IDW data wll come back prevous state and construct the orgnal data Hard hresholdng In the case of hard thresholdng: D(Y, λ)º 3... Soft hresholdng Y f Y > λ otherw se In the case of soft thresholdng, or Wavelet shrnkage: D(Y, λ)º Bayes Shrnk sgn(y)( Y - λ) f Y > λ otherwse he observaton model s Y = X + V, wth X and V ndependent of each other, hence: Y X σ = σ + σ (6) Where the nose varance σ s estmated from the subband HH by the robust medan estmator [4]: Medan( Y ) j σ =, Y subband HH (7) j.6745 And σ Y s the varance of Y. Snce, Y s modeled as zero-mean, σ Y can be found emprcally by: n ˆσ Y = Y j n, j = (8) Where n n s the sze of the subband under consderaton. hus: Where: ˆ ˆ ˆ ˆσ ˆ B ( σ ˆ X ) = ˆσ X σ X = max(σ Y - σ, ) (4) (5) (9) 4. Proposed Method 4.. Objectve Functon Frstly dscrete wavelet transform s appled on an mage for creatng the subband coeffcent. An mage s f(x, y) and the sze of mage s M N then DW s: Fgure. wo-level decomposton of Lena mage. 3.. Wavelet Shrnkage Let W(.) and W - (.) denote the forward and nverse wavelet transform operators. Let D(., λ) denote the thresholdng operator wth threshold λ. he practce of thresholdng denosng conssts of the followng three steps: Step : Y=W(x) Step : Z=D(Y, λ) Step 3: xˆ = W (Z) Hard thresholdng and soft thresholdng are only dfferent n step. Where: = {H,V,D} M - N - W ψ (j, m, n) = f(x, y) ψ j,m,n (x, y) MN x= y= A3 H3 V3 D3 V V Fgure 3. Subbands of the D orthogonal wavelet transform. Where (H, V, D); (H, V, D) and (H3, V3, D3) are, and 3 scale wavelet coeffcent subband respectvely. Indvdually each coeffcent s denoted by n. otal number of coeffcent N = n + n + n + H D H D (3)

4 576 he Internatonal Arab Journal of Informaton echnology, Vol., No. 6, November 4 + n M. Now, we have to calculate each coeffcent probablty usng below ths equaton: Where: M P = = n P = ; P N Suppose that the coeffcents are dvded nto two classes C and C by a fxed value t; C s the set of coeffcents wth levels [,,..., L], and the rest of coeffcents belong to C. C and C normally correspond to the object class and the back ground one, or vce versa. hen, the probabltes of the two classes are gven by wthn: L W ( L ) = = P W ( L ) = - W ( L ) he mean coeffcents of the two classes can be defned as: µ = µ = L P = W M P = L + W Correspondng class varances are gven by: L ( - µ ) P = W σ = M ( - µ ) P σ = = L + W he wthn-class varance can be defned []: σ W = W σ + W σ As we have seen n secton., the FLD seeks drectons effcent for dscrmnaton by yeldng the maxmum rato of between-class scatter to wthn-class scatter. hus, Based on the functon defned by Equaton 9 the followng crteron as objectve functon to evaluate the separablty of the threshold at level L. Where: σ W = W σ + W σ (µ (L) - µ (L)) ρ(l) = σw (3) (3) (33) (34) (35) (36) From Equaton 33 we shall get FDA thresholdng value between two classes as follows. can be used for separatng two classes but, f we want to apply threshold value for nose reducton then ths type of thresholdng can not be effcent for nose reducton. hese stuatons we can overcome by applyng the standard devaton and mean value rato of the coeffcent of any subband of the wavelet. Here we proposed the proper threshold value estmaton method for speckle nose reducton n the wavelet doman. So, ths method s gven below. If the dscrete wavelet transform of functon s ξ (x, y) and the mage sze s F H then the mean value of the wavelet coeffcent s: µ c = ξ (x, y ) F H Where: ={H,V,D} And the standard devaton of the wavelet coeffcent s: σ c = F H [ ξ ( x, y ) µ c ] x = y = F H For the large FDA threshold value huge amount of dagnostc nformaton s lost. o remove ths lmtaton we use mathematcal operatons between mean and standard devaton of wavelet coeffcents wth respect to FDA threshold value to obtan an optmal threshold value. he proposed optmal threshold value s: o p t m a l = σ c Where: σ c > µ c Now, we get optmal threshold value from Equaton 36 usng FDA for speckle nose reducton of ultrasound mages. We know ξ ( x, y) s the dscrete wavelet coeffcent and optmal threshold value s optmal. Optmal threshold operaton on wavelet coeffcent s shown below: µ c If ξ (x, y) < ={H,V,D} then End optm al ξ (x, y ) = able. For Lver ultrasound mage. Method SNR EPF MSE FDA thresholdng () FDA optmal thresholdng ( optmal) (37) (38) (39) We use Lena mage for testng the performance between FDA thresholdng and FDA optmal thresholdng. From able we see that FDA optmal thresholdng exhbts better performance than FDA thresholdng. Here we show the hstogram comparson and effcency of those threshold values. From Fgure 4, we see that Fgure 4-b lost ts structural vew but, Fgure 4-c has a structural vew wth respect to orgnal mage. We observe that FDA optmal threshold show the better performance for edge preservaton over exstng FDA threshold. Very small amount of error occurred n the fltered mage for FDA optmal thresholdng technque and enhance the mage clearly. From these measurements, we can comment that FDA optmal threshold performance sgnfcantly better than FDA threshold.

5 Optmum hreshold Parameter Estmaton of Wavelet Coeffcents Usng Fsher Dscrmnant Analyss for Orgnal mage mage a) Orgnal Lena mage. b) After FDA thresholdng. c) After FDA optmal thresholdng. Fgure 4. Hstogram of Lena mage wth FDA thresholdng operaton. 4.. Algorthm Followng steps descrbe the proposed algorthm for mage denosng:. Let max p =, be the maxmum value of the objectve functon.. For k = to Maxmum of coeffcent value. 3. Compute the objectve functon value correspondng to the coeffcent value k: I f max ρ < ρ(k) End then max ρ = k = ρ(k) 4. he optmal threshold value estmaton for denosng n wavelet feld: Where: σ c > µ c o p t m a l = σ c µ c 5. Wavelet coeffcent s denoted by W c and Optmal threshold value performance s: If Wc< optmal then Wc= End 5. Evaluaton Crtera We observe the performance by apply Sgnal to Nose Rato (SNR), Mean Square Error (MSE) and Edge Preservaton Factor (EPF) parameter [4]. Sgnal to Nose Rato (SNR): SNR = -log FDA optmal FDA threshold M N x = y = (I d (x, y) - I(x, y)) M N x = y = (I d (x, y)) he edge preservaton ablty of the flter s compared by EPF and s computed usng EPF: FDA FDA threshold (4) Where I and I d are the hgh pass fltered versons of mages I and I d, obtaned wth a 3 3 pxel standard approxmaton of the Laplacan operator. he larger value of EPF means more ablty to preserve edges. MSE: MSE = M - N - x = y = (I(x, y) - I d (x, y)) M N (4) Where the mage sze s M N. x means row, y means column, I means orgnal mage and I d means fltered mage. 6. Expermental Result he proposed algorthm has been appled to D ultrasound mage wth have been corrupted by multplcatve nose (speckle nose of varance.4). he computaton s carred out on MALAB (Ra) n a Core duo.33ghz and GB RAM desktop havng a Wndows operatng system. We choose four mages (e.g., Cameraman, Lena, Kdney, Lver) for testng the performance of the proposed algorthm. Our proposed algorthm s compared wth exstng method whch s shown n ables and 3 and Fgures 8, 9 and respectvely. Method Wavelet Hard hreshold Wavelet Soft hreshold Bayesan hreshold FDA Denosng Method Wavelet Hard hreshold Wavelet Soft hreshold Bayesan hreshold FDA Denosng able. For cameraman and lena mages. Cameraman Lena SNR EPF MSE SNR EPF MSE able 3. For ultrasound kdney and lver mages Kdney Lver SNR EPF MSE SNR EPF MSE Expermental numercal results show the mproved speckle nose reducton capabltes of the proposed FDA optmal threshold based flterng compared to the classcal methods. From ables and 3, we see that our proposed flter effectvely and properly remove speckle nose from ultrasound mages because a small amount of error s occurred n the flter mage and the proposed method s shown the mentonable edge preservaton. Hstogram of the wavelet coeffcent s gven below: E PF = ( I - I )( I d - I d ) ( I - I ) ( I d - I d ) (4)

6 578 he Internatonal Arab Journal of Informaton echnology, Vol., No. 6, November scale horzontal scale vertcal scale scale dagonal scale horzontal scale dagonal scale scale horzontal scale scale vertcal scale scale dagonal a) Hstogram of Cameraman mage. scale scale horzontal scale scale vertcal scale scale dagonal scale scale horzontal scale scale vertcal vertcal scale scale dagonal Detal. Dagonal subbands are more senstve for optmal threshold value estmaton and nose analyss or reducton. Probablty densty curve of orgnal mage and flter mage s gven below: Orgnal mage 3 Flter mage a) Probablty densty curves of Cameraman mage. Orgnal mage Orgnal mage Flter mage flter mage 4 4 b) Probablty densty curves of Lena mage Orgnal mage Orgnal mage.35 Flter mage flter mage b) Hstogram of Lena mage. c) Hstogram of Kdney mage. - - scale scale horzontal scale scale vertcal vertcal scale scale dagonal scale scale horzantal horzontal scale scale vertcal vertcal scale scale dagonal scale scale horzantal horzontal scale scale vertcal vertcal scale scale dagonal scale scale horzantal horzontal scale scale vertcal scale scale dagonal dagonal c) Probablty densty curves of Kdney mage. Orgnal mage Orgnal mage Flter mage d) Probablty densty curves of Lver mage. Fgure 6. Probablty densty curves of four test mages. We can see that from the probablty densty curves Fgure 6 of orgnal and flter mages, very small change between two curves. So, we can say that a small amount of nformaton s lost and very small amount of error s occurred n the flter mage. Naturally flter mage s so structural that means the edge preservaton and smoothness of the flter mage s really good wth respect to orgnal mage. Mean and varance curves of two classes (e.g. between class scatter, wthn class scatter) only for dagonal (D) subbands are gven below flter mage d) Hstogram of Lver mage. Fgure 5. Hstogram of the wavelet coeffcents of four test mages. Fgure 5 manly depcts the coeffcent varaton of the wavelet domans by the hstograms. We observe from these hstograms that the coeffcent varaton of the dagonal subband s always smaller than other

7 Optmum hreshold Parameter Estmaton of Wavelet Coeffcents Usng Fsher Dscrmnant Analyss for 579 Scale Mean scale Mean a) Mean curves of Cameraman mage for the frst level dagonal Scale Varance scale Varance x a) Kdney ultrasound nosy mage. b) Hard hresholdng b) Varance curves of Cameraman mage for the frst level dagonal. 5 Scale Mean scale Mean c) Soft hresholdng. d) BayesShrnk c) Mean curves of Cameraman mage for the second level dagonal. 3 scale Scale Varance varance 3 x d) Varance curves of Cameraman mage for the second level dagonal. Fgure 7. Mean and varance curve of dagonal coeffcent of Cameraman mage. Fgure 7 s used for measurng the central tendency to the natural or orgnal structure of the fltered data of between class scatter and wthn class scatter usng mean value and varance. Vsual qualty comparson s gven below for levels:.5.5 e) Bayesan hresholdng. f) FDA Denosng. Fgure 9. Vsual comparson of Kdney ultrasound mage after executon some exstng state-of-the-art flters and our proposed flter on Kdney ultrasound nosy mage. a) Lver ultrasound nosy mage. b) Hard hresholdng. c) Soft hresholdng. d) BayesShrnk. a) Lena nosy mage. b) Hard hresholdng. c) Soft hresholdng. d) BayesShrnk. e) Bayesan hresholdng. f) FDA Denosng. Fgure 8. Vsual comparson of Lena mage after executon some exstng state-of-the-art flters and our proposed flter on Lena nosy mage. e) Bayesan hresholdng. f) FDA Denosng. Fgure. Vsual comparson of Lver ultrasound mage after executon some exstng state-of-the-art flters and our proposed flter on Lver ultrasound nosy mage. From Fgures 8, 9, and, proposed fltered mage vsual qualty s absolutely good because our proposed algorthm shows better performance for speckle nose reducton. From the observaton of the proposed fltered mage, we see that t s so smooth and enhance over exstng despeckle methods mages and ts has no any checker board and blurrng effect n the

8 58 he Internatonal Arab Journal of Informaton echnology, Vol., No. 6, November 4 homogeneous regons but preserve edges sgnfcantly wthout destroyng vtal nformaton of the mage. 7. Conclusons We have proposed an effectve method for speckle denosng va wavelet transformaton usng FDA proposed optmal threshold value. Our method exhbts better performance n comparson to exstng methods for speckle nose reducton, edge preservaton, vsual qualty and mean squared error. Our proposed method s especally effectve for hghly nhomogeneous mage and can be used wdely for speckle nose reducton of speckle affected mages. References [] Achm A., Bezerano A., and asakaldes P., Novel Bayesan Multscale for Speckle Removal n Medcal Ultrasound Images, IEEE ransactons on Medcal Imagng Journal, vol., no. 8, pp ,. [] Azm G. and Abo-Eleneen Z., hresholdng based on Fsher Lnear Dscrmnant, Journal of Pattern Recognton Research, vol. 6, no., pp ,. [3] Donoho D. and Johnstone I., Adaptng to Unknown Smoothness va Wavelet Shrnkage, Journal of Amercan the Denosng Performance. Statstcal Assoc., vol. 9, no. 43, pp. - 4, 995. [4] Donoho D. and Johnstone I., Ideal Spatal Adaptaton va Wavelet Shrnkage, Bometrca, vol. 8, no. 3, pp , 994. [5] Donoho D. and Johnstone I., Wavelet Shrnkage: Asymptopa, Journal of the Royal Statstcal Socety. Seres B, vol. 57, no., pp , 995. [6] Fodor I. and Kamath C., Denosng hrough Wavelet Shrnkage, Journal of Electronc Imagng, vol., no., pp. 5-6, 3. [7] Grace C., Yu B., and Vatterel M., Adaptve Wavelet hresholdng for Image Denosng and Compresson, IEEE ransacton Image Processng, vol. 9, no. 9, pp ,. [8] Grace C., Yu B. and Vatterel M., Spatally Adaptve Wavelet hresholdng wth Context Modelng for Image Denosng, IEEE ransacton Image Processng, vol. 9, pp. 5-53,. [9] Grace C., Yu B., and Vatterel M., Wavelet hresholdng for Multple Nosy Image Copes, Journal of IEEE ransacton Image Processng, vol. 9, pp ,. [] Jansen M., Nose Reducton by Wavelet hresholdng, Sprnger-Verlag, New York, USA,. [] Muhsen Z., Dababneh M., and Nsour A., Wavelet and Optmal Requantzaton Methodology for Lossy Fngerprnt Compresson, the Internatonal Arab Journal of Informaton echnology, vol. 8, no. 4, pp ,. [] Otsu N., A hreshold Selecton Method from Gray-Level Hstograms, IEEE ransacton System Man Cybern, vol. 9, no., pp 6-66, 979. [3] Rajan J. and Kamal M., Image Denosng Usng Wavelet Embedded Ansotropc Dffuson (WEAD), n Proceedngs of IEEE Internatonal Conference on Vsual Engneerng(VIE), London, UK, pp , 6. [4] Sattar F., Floreby L., Salomonsson G., and Lovstorm B., Image Enhancement Based on a Nonlnear Multscale Method, IEEE ransactons on Image Processng, vol. 6, no. 6, pp , 997. [5] Shaho B., Wang Y., Deng X., and Wang S., Sparse lnear Dscrmnant Analyss by hresholdng Hgh Dmensonal Data, he Annals of statstcs, vol. 39, no., pp. 4-65,. [6] Vatterel M. and Kovacevc J., Wavelets and Subband Codng. Englewood Clffs, Prentce Hall, New Jersy, USA, 995. [7] Wu H. and Huang D., Kernel Fsher Dscrmnant Analyss Usng Feature Vector Selecton for Fault Dagnoss, n proceedngs of the nd IEEE nternatonal symposum on ntellgent nformaton technology applcaton, Shangha, Chna, pp.9-3, 8. Mohammad Motur Rahman receved hs BSc Engneerng and MSc degree n computer scence and engneerng from Jahangrnagar Unversty, Bangladesh, n 995 and, where he s currently pursung the PhD degree. Hs research nterests nclude dgtal mage processng, medcal mage processng, computer vson and dgtal electroncs. He has many nternatonal journal and conference publcatons. Mthun Kumar PK he receved hs BSc engneerng degree n computer scence and engneerng from Mawlana Bhashan Scence and echnology Unversty, Bangladesh. Hs research nterests nclude mage analyss, mage processng and medcal mage processng, pattern recognton, 3D vsualzaton, segmentaton, flter optmzaton. He has many nternatonal journal and conference publcatons and He s a regular revewer of IE mage processng journal.

9 Optmum hreshold Parameter Estmaton of Wavelet Coeffcents Usng Fsher Dscrmnant Analyss for 58 Mohammad Shorf Uddn s currently workng n the Department of Computer Scence and Engneerng, Jahangrnagar Unversty, Bangladesh. Hs research s focused on bomagng and mage analyss, computer vson, pattern recognton, blnd navgaton, medcal dagnoss, and dsaster preventon. He publshed many papers n renowned journals lke IEEE, Elsever, IE, Optcal Socety of Amerca etc.