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International Journal of Computer Information Systems, Vol. 1, No. 5, 2010 A Study on the Application of Wavelets for Despeckling Ultrasound Images K. Karthikeyan Dr. C. Chandrasekar Assistant Professor, Associate Professor, Department of Information Technology, Department of Computer Science, Dr. SNS Rajalakshmi College of Arts & Periyar University, Science, Coimbatore, India. Salem, TN, India. Abstract : Medical digital images, produced by various Images produced by these devices can be imaging devices like x-ray, CT / MRI scanners, ultrasonic, displayed, captured, and broadcast through a computer etc., have become an essential part in the healthcare using a frame grabber to capture and digitize the analog industry for diagnosis of diseases. The main problem video signal. The captured signal can then be post- during diagnosis is the distortion of visual signals obtained due to imperfect acquisition and transmission errors. processed on the computer itself. Ultrasonography is These distortions are termed as ‘Noise’. This study focus inexpensive and portable when compared with other on one type noise, namely, ‘Speckle Noise’, produced by imaging techniques such as Magnetic Resonance Imaging ultrasonic devices. This paper considers wavelets to reduce (MRI) and Computerized Tomography (CT) [5]. It is speckle noise and the studies the effect of various wavelets widely used by practitioners as they have no known long- (Haar, D4 and Coiflets) at different decomposition levels term side effects and has the added advantage that it is (I, II, III and IV) for three different threshold shrinking non-intrusive to the patients [15]. The device provides techniques, VisuShrink, SureShrink, BayesShrink. The live images, where the operator can select the most useful experimental results proved that wavelets are indeed a section for diagnosing thus facilitating quick diagnoses perfect solution to despeckle images. The best performance was obtained for level I decomposition and as the level of [20]. decomposition increased, artifacts and distortions One of the major problems of ultrasound images appeared in the images. Out of the three wavelets is that they suffer from a special kind of noise called considered Coiflets produced best results. The 'speckle'. Speckle is a complex phenomenon and it performance of BayesShrink was superior to that of VisuShrink and SureShrink. significantly degrades image quality. Speckle appears interference of back-scattered wave from many Keywords : Speckle Noise, wavelets, BayesShrink, microscopic diffused reflection which passing through VisuShrink, SureShrink internal organs and makes it more difficult for the 1. INTRODUCTION observer to discriminate fine detail of the images in diagnostic examinations. Medical digital images have become an essential part in the healthcare industry for diagnosis of Generally speaking there are two techniques of diseases. These images are produced by various medical removing/reducing speckle noise, i.e., multi-look process imaging devices like x-ray, CT / MRI scanners and and spatial filtering. Multi-look process is used at the electron microscope all of which produce high data acquisition stage while spatial filtering is used after resolution images. However, imperfect acquisition the data is stored. No matter which method is used to instruments, transmission errors often distort the visual reduce/remove the speckle noise, they should preserve signals obtained. These distortions are referred to as radiometric information, edge information and last but “Noise” and have to be removed to improve the quality not least, spatial resolution ([1], [18]). In simple terms, of the image. The techniques used to remove noise are the goal of any speckle removal algorithm should be to termed as “Image Denoising”. Image denoising, a well- enhance the corrupted images by maintaining the quality studied problem in computer vision for natural images, of the image. is still in infantry stage where medical imaging is This paper is an effort made to produce a concerned. It is the most sought after tool by the image speckle noise removal technique based on wavelets with analysts in the fast-growing medical field, as noisy twofold objectives, namely maintain quality while strong images often lead to incorrect diagnosis. edge sharpness. The paper is organized as below. The Diagnostic sonography or ultrasonography is second section gives an overview to the noise under an ultrasound-based diagnostic imaging technique used discussion, while Section 3 discusses the existing to visualize subcutaneous body structures including solutions. Section 4 presents the proposed algorithm and tendons, muscles, joints, vessels and internal organs for the performance of the proposed algorithm is presented in possible pathology or lesions. Obstetric sonography is Section 5. Section 6 presents a short conclusion with commonly used during pregnancy and is widely future research direction. recognized by the public (www.wikipedia.org). Medical 2. SPECKLE NOISE sonography is used in the study of many different systems like cardiology, gastroenterology, gynecology, Speckle is a random, deterministic, interference neurology, obstetrics, urology and cardiovascular pattern in an image formed with coherent radiation of a systems [22]. medium containing many sub-resolution scatterers. December Issue Page 48 of 69 ISSN 2229 5208 International Journal of Computer Information Systems, Vol. 1, No. 5, 2010 Speckle has a negative impact on ultrasound imaging. Further, the speckle noise is a high-frequency component The presence of speckle noise in images shows a of the image and appears in wavelet coefficients. reduction of lesion detectability of approximately a Wavelets attempt to remove the noise present while factor of eight [4]. This radical reduction in contrast preserving the important features, independent of its resolution is responsible for the poorer effective frequency content. As the discrete wavelet transform resolution of ultrasound compared to x-ray and MRI. (DWT) corresponds to basis decomposition, it provides a Presence of speckle noise prevents Automatic Target non-redundant and unique representation of the signal. Recognition (ATR) and texture analysis algorithm to perform efficiently and gives the image a grainy 3. Wavelet based Speckle Denoising Model (WSD) appearance. Hence, despeckling is considered as a Wavelet approach for noise removal has been critical pre-processing step in medical imaging systems. successfully exploited by several researchers ([17], [8], Speckle noise follows a gamma distribution and is given [12]) in the past few decades. It has been proved that the as in Equation (1). use of wavelets successfully removes noise while preserving t content. A wavelet denoising model can be 1 g represented by the Equation 3. g F( g ) e a (1) I(t) = O(t) + N(t) (3) ( 1)! a where O(t) represents the original noise free data, N(t) is where variance is aα and g is the gray level. On an the speckle noise. Let W(f) and Wi'(f) denote the forward and inverse wavelet transform operators. Let D(f, ) image, speckle noise (with variance 0.05) looks as denote the denoise operator with threshold . The main shown in Figure 1a and the corresponding gamma aim of the denoising procedure is to denoise I(t) to distribution is given in Figure 1b. recover O'(t). A General WSD model is shown in Figure 2. The WSD model consists of three main steps after image acquisition. The first step is a linear forward Discrete Wavelet Transform (DWT), followed by a non- linear thresholding step and the final step performs a linear Inverse Discrete Wavelet Transform (IDWT). (a) Speckle Noise (b)Gamma Distribution Figure 1 : Noise and Distribution Noisy DeNoised Input Ouput Mathematically, a speckle noise can be represented by DWT IDWT the Equation 2. Thresholding S' = FS (2) (i) Shrinkage Rule – Calculate Threshold where S' (=s1', s2', …) is the speckled image, F (ii) Shrinkage Function – Apply (=f1, f2, …) is the noise free image and S (=s1, s2, …) is Threshold the speckle noise introduced. The corrupted pixels are Figure 2 : WSD Model either set to the maximum value, which is something like a snow in image or have single bits flipped over. a) Discrete Wavelet Transform (DWT) These noisy data can be reduced or removed using specially designed filters and are discussed in the next 1 2 5 1 2 LL1 HL2 5 section. Several adaptive filters have been implemented 3 4 3 4 8 for speckle noise removal and some examples include LH3 HH4 6 7 6 7 Lee filter, Frost filter, Kaun Filter and Kuwahara Filter. (a) 1- Level (b) 2- Level Most of these proposed local adaptive speckle 10 9 filters are able to reduce speckle while preserving the 1 2 5 data. However, all these uses a lossy approach, as all 3 4 8 these filters rely on local statistical data related to the 6 7 9 (c) 3- Level filtered pixel. This data depends on the occurrence of the filter window over an area. The achievement of both 9 10 speckle reduction and preservation of edge data is only Figure 3 : possible when the filter window is uniform. If the filter Image window happens to cover an edge, the value of the Decomposition filtered pixel will be replaced by the statistical data from 10 11 both sides of the edge that is from two different intensity distributions. An alternative approach is to use wavelet transform. The popularity of wavelets to despeckle is (d) 4- Level because the wavelet transforms does not rely on any The first step in WSD model is the selection of fixed window size and instead the window size is the forward and inverse wavelet transformation. A variable depending on the contents of the image. variety of wavelets transformation techniques are December Issue Page 49 of 69 ISSN 2229 5208 International Journal of Computer Information Systems, Vol. 1, No. 5, 2010 available for the purpose of denoising. Some of them include Haar, Daubeschies, Coiflets, Symlets, Morlets, Mexican Hat, Meyer and Biorthogonal wavelets [16]. The present study considers Haar, Daubeschies and Coiflets into consideration for denoising. Application of DWT divides an image into four subbands (Figure 3), which arise from separable applications of vertical and horizontal coefficients. The LH, HL and HH subbands (a) Original Signal (b) Hard Threshold (c) Soft Threshold represents detailed features of the images, while LL Figure 4 : Effect of Thresholding subband represents the approximation of the image. To obtain the next coarse level, the LL subband can further be decomposed (Figure --b), thus resulting in the 2-level The hard threshold work on the “Kill or Keep” wavelet decomposition. The level of decomposition principle where the input is kept, if it is greater than a performed is application dependent. The present work defined threshold () otherwise it is set to zero. It considers upto four level of decomposition. The removes noise by thresholding only the detailed subband advantages of using wavelets for denoising are wavelet coefficients, while keeping the low-resolution multifolded. The first is that different sized images at coefficients unaltered. An extension to hard thresholding different resolution can be analyzed, the coefficients are is the soft thresholding, which works on the “Shrink or small in magnitude and the large coefficients coincide Keep” principle. The output is forced to zero, if the with image edges. The edge coefficients within each absolute value of I is less than the threshold else the subband tend to form spatially connected clusters. output is set to |I-|. The effect of hard and soft b) Thresholding thresholding on an original signal is given in Figures 4a,b,c. Discontinuities at is seen with hard The second step in the WSD model is the thresholding and they are more sensitive to small selection of a wavelet thresholding technique. ([6], [9], changes, while soft threshold avoids both these [10]). Wavelet thresholding is a signal estimation situations. Thus the advantages of soft thresholding are it technique that exploits the capabilities of wavelet reduces abrupt sharp changes and provides an image transform for signal denoising. It removes noise by whose quality is not degraded. Because of these killing or shrinking coefficients that are insignificant advantages, soft thresholding is more frequently used. relative to some threshold. They are simple yet effective Once the thresholding operator has been defined, the next and depend heavily on the thresholding parameter. The step is to address the problem of selecting the efficiency of WSD greatly depends on the correct choice corresponding threshold. of parameter. Wavelet thresholding is composed of two steps namely, thresholding method and threshold (ii) Selection of threshold selection. The selection of threshold is the most important (i) Threshold operators step in any WSD model. Careful selection is needed because a small threshold will produce an image which is Most frequently used thresholding methods are still noisy, while a large threshold destroys details and soft and hard thresholding [13]. The hard and soft produces blurs and artifacts. Two types of thresholding thresholding operations are defined as in Equations (4) techniques, namely, Universal Thresholding (UT) and and (5). Subband Adaptive Thresholding (SA) exists. UT was I for all | I | (4 proposed by Donoho and Johnstone in 1995 [10] where Thard ( I, ) ) the threshold is calculating as in Equation 6. 0 otherwise 2 log(M) (6) sign( I) max(0, | I | - for all | I | (5 Tsoft ( I, ) ) 0 otherwise where is the local noise variance in each subband of the speckle image after decomposition and M is the block size in the wavelet domain. The estimated noise variance in each subband is obtained by finding the average of squares of the wavelet coefficients at the highest resolution scale (Equation 7) N 1 2 (X j ) (7) i 0 N The three famous threshold calculating techniques, namely, VisuShrink [11], SureShrink [10] December Issue Page 50 of 69 ISSN 2229 5208 International Journal of Computer Information Systems, Vol. 1, No. 5, 2010 and BayesShrink [7]. VisuShrink uses the universal threshold level is assigned to each dyadic resolution level thresholding, while SureShrink and BayesShrink uses by the principle of minimizing the Stein‟s Unbiased Risk data drive adaptive technique. Estimator for threshold estimates. It is smoothness adaptive, which means that if the unknown function VisuShrink Thresholding contains abrupt changes or boundaries in the image, the VisuShrink uses a threshold value „t‟ that is reconstructed image also does. proportional to the standard deviation of the noise. It BayesShrink Thresholding follows the hard, universal thresholding rule and is defined by the Equation (8). The goal of BayesShrink method is to minimize the Bayesian risk, and hence its name, BayesShrink. It t 2 log n (8) uses soft thresholding and is subband-dependent, which means that thresholding is done at each band of where σ is the noise variance present in the signal and n resolution in the wavelet decomposition. Like the represents the signal size or number of samples. An SureShrink procedure, it is smoothness adaptive. The estimate of the noise level σ was defined based on the Bayes threshold, tB, is defined as median absolute deviation [Do94] given by tB = 2/s2 (12) j1 median (| g j1, k |) where k 0,1,..., 2 1 ˆ (9) where σ2 is the noise variance and σs2 is the signal 0.6745 variance without noise. The noise variance σ2 is where gj-1,k corresponds to the detail coefficients in the estimated from the subband HH1 by the median estimator wavelet transform. shown in Equation (9). From the definition of additive noise, VisuShrink does not deal with minimizing the mean squared error. It can be viewed as general-purpose w(x, y) = s(x, y) + n(x, y) (13) threshold selectors that exhibit near optimal minimax Since the noise and the signal are independent of each error properties and ensures with high probability that other, it can be stated that the estimates are as smooth as the true underlying functions. However, VisuShrink is known to yield σ2w =σ2s + σ2w (14) recovered images that are overly smoothed. This is because VisuShrink removes too many coefficients. σ2w can be computed using Equation (15). From this the Another disadvantage is that it can only deal with an variance of the signal, σ2s can be computed using additive noise. VisuShrink follows the global Equation (16).. thresholding [2] scheme where there is a single value of threshold applied globally to all the wavelet coefficients. 1 n 2 w 2 w ( x , y) (15) 2 SureShrink Thresholding n x , y 1 A threshold chooser based on Stein‟s Unbiased s max( 2 2 ,0) (16) w Risk Estimator (SURE) is called as SureShrink. It is a combination of the universal threshold and the SURE with σ2 and σ2s, the Bayes threshold is computed from threshold. This method specifies a threshold value tj for Equation (12). each resolution level j in the wavelet transform which is referred to as level dependent thresholding [2]. The goal of SureShrink is to minimize the mean squared error 4. DENOISING EXPERIMENTS (Equation 10). The selection of the denoising technique is 1 n 2 application dependent and therefore, it is necessary to MSE (z( x, y) s( x, y)) (10) n 2 x , y 1 learn and compare denoising techniques to select the technique that is apt for the application of interest. where z(x,y) is the estimate of the signal while s(x,y) is Several experiments were conducted to evaluate the the original signal without noise and n is the size of the denoising techniques based on three DWT techniques signal. SureShrink suppresses noise by thresholding the (Haar, D4-Daubeschies and Coiflets) for four empirical wavelet coefficients. The SureShrink decomposition levels (1-4) with three different shrinking threshold t* (Equation 11). techniques (VisuShrink, SureShrink and BayesShrink). The models proposed are given in Table 1. t* min( t, 2 log n ) (11) Table 1 : Proposed denoising models Level of Shrinking Model where t denotes the value that minimizes Stein‟s Wavelet Used Decomposition Method Code Unbiased Risk Estimator, σ is the noise variance H1VS, computed from Equation (4.9), and n is the size of the H2VS, image. SureShrink follows the soft thresholding rule. Haar I, II, III, IV VisuShrink H3VS, The thresholding employed here is adaptive, i.e., a H4VS December Issue Page 51 of 69 ISSN 2229 5208 International Journal of Computer Information Systems, Vol. 1, No. 5, 2010 H1SS, A. Mean Square Difference (MSD) H2SS, SureShrink MSD indicates average square difference of the H3SS, pixels throughout the image between the original image H4SS (with speckle) (Is) and denoised image (Id ). A lower H1BS, MSD indicates a smaller difference between the original H2BS, (with speckle) and despeckled image. This means that BayesShrink H3BS, there is a significant filter performance. Nevertheless, it H4BS is necessary to be very careful with the edges. The D1VS, formula for the MSD calculation is given in Equation D2VS, (17) VisuShrink D3VS, D4VS (I s (r, c) I d (r, c)) 2 D1SS, MSD r, c (17) D2SS, R *C Daubeschies I, II, III, IV SureShrink D3SS, B. Noise Mean Value (NMV), Noise Variance (NV), D4SS and Noise Standard Deviation (NSD) D1BS, D2BS, NV determines the contents of the speckle in the image. BayesShrink A lower variance gives a “cleaner” image as more D3BS, D4BS speckle is reduced and the formulas for the NMV, NV C1VS, and NSD calculation are given in Equations (18) to (20). C2VS, I d ( r , c) (18) VisuShrink C3VS, NMV r ,c C4VS R *C C1SS, 2 (19) (I d (r, c) NMV) C2SS, Coiflets I, II, III, IV SureShrink NV r, c C3SS, R *C C4SS C1BS, NSD NV (20) C2BS, BayesShrink C3BS, where I is the image, r and c are the number of rows and C4BS columns in the noisy image, while its corresponding R Original Image Speckle Image and C is the number of rows columns in the denoised image. The product R*C represents the size of the despeckled image Id. On the other hand, the estimated noise variance is used to determine the amount of smoothing needed for each case for all filters. C. Equivalent Numbers of Looks (ENL) Figure 5 : Test Image Another good approach of estimating the All the models were tested with the test image speckle noise level in an ultrasonic image is to measure (grayscale) of 256 x 256 size (Figure 5). The proposed the ENL over a uniform image region [21]. A larger models were implemented using MATLAB 7.3 and value of ENL usually corresponds to a better quantitative were tested on Pentium IV machine with 512 MB RAM. performance. The value of ENL also depends on the size Mastriani and Giraldez [19] used six quality parameters, of the tested region, theoretically a larger region will namely, (i) Noise Mean Value (ii) Noise Variance (iii) produces a higher ENL value than over a smaller region Noise Standard Deviation (iv) Mean Square Difference but it also tradeoff the accuracy of the readings. Due to (v) Equivalent Number of Looks and (vi) Deflection the difficulty in identifying uniform areas in the image, Ratio. Out of this, (iii) is calculated from one and two the image is first divided into smaller areas of 25x25 and hence, only (iii) is considered in the present work. pixels and the ENL for each of these smaller areas is Deflection ratio is used to measure the quality of the obtained, whose average gives the final ENL value despeckled image, it was replaced by a another simple (Equation 21). parameter, Peak Signal to Noise Ratio (PSNR). Thus, to evaluate the despeckling performance of DWT with NMV 2 ENL (21) respect to four levels and three shrinkage techniques, the NSD 2 following parameters were used. (i) Mean Square Difference (ii) Noise Standard Deviation (ii) Equivalent The significance of obtaining both MSD and ENL Number of Looks and (iv) PSNR. For easy measurements in this work is to analyze the performance understanding, the metrics are explained below. of the filter on the overall region as well as in smaller uniform regions. December Issue Page 52 of 69 ISSN 2229 5208 International Journal of Computer Information Systems, Vol. 1, No. 5, 2010 D. Peak Signal to Noise Ratio C3VS 776.3985 32.7772 37.1294 36 PSNR is often used as a quality measurement C4VS 777.1002 32.8109 27.1105 36 between the original and a compressed image. The C1SS 748.9854 32.7399 38.9891 44 higher the PSNR, the better the quality of the C2SS 749.3651 32.9999 37.1149 42 compressed, or reconstructed image. C3SS 749.8947 33.1538 36.6655 42 To compute PSNR, the block first calculates C4SS 749.8964 33.2188 36.7135 42 the Mean-Squared Error (MSE) and then the PSNR C1BS 720.7694 29.9584 39.2884 46 (Equation 22). C2BS 720.9328 30.9999 39.1672 45 C3BS 721.7473 31.2694 38.9549 45 PSNR = 10 log10 R 2 C4BS 722.0909 31.2932 39.0048 45 MSE From the results obtained, it can be seen that [I1 (m, n ) I 2 (m, n )] 2 (22) that the Coiflets transformation is better than the other where MSE = M, N where M*N two transformation techniques. Similarly, the quality of M and N, m and n are number of rows and despeckled image was good with level 1 decomposition. columns in the input and output image Our results are similar to the results obtained by [3] who respectively reported that highest PSNR can be obtained with first level of DWT decomposition for most of the speckle 4.1. RESULTS noise added images, further severe blurring occurs as the The mean square difference, noise standard level of decomposition is increased. Similarly, [14] found deviation, equivalent number of looks and PSNR out that Coiflets transformation performs better than D4 obtained during experimentation is presented in Table and Haar. The high PSNR obtained by BayesShrink in 2a and 2b. all the decomposition level indicates that it is the best Table 2a : Experimental Results choice for removing speckle noise from ultrasound images. Figure 6 visually compares the result between Model MSD NSD ENL PSNR the three shrinkage methods for first level of H1VS 798.4422 32.8123 37.0843 33 decomposition. Figure 6 shows the result of BayesShrink H2VS 797.8754 32.8894 35.1871 31 for all the four levels using Coiflets transform. H3VS 797.9193 33.4781 34.6591 30 H4VS 798.2210 33.0411 34.7181 30 H1SS 761.8832 32.8990 37.6666 40 H2SS 762.9872 32.9299 36.4344 39 H3SS 763.0003 33.9863 35.1200 39 H4SS 760.2834 33.9833 35.1209 39 H1BS 733.3256 31.7981 38.0013 45 (a) VisuShrink (b) SureShrink H2BS 732.8319 32.9307 37.6721 43 H3BS 732.8777 33.0992 37.4329 42 H4BS 733.1891 33.9381 37.2111 42 D1VS 782.3323 32.7812 38.0843 31 D2VS 783.0054 33.0091 36.2569 30 D3VS 783.1033 33.5301 34.4432 29 D4VS 783.1987 33.9864 34.1256 29 (C) BayesShrink D1SS 754.6344 32.8978 38.4325 36 Figure 6 : Visual Result D2SS 753.6632 32.2381 37.6700 37 Table 2b : Experimental Results 5. CONCLUSION Model MSD NSD ENL PSNR From the exhaustive experiments, conducted D3SS 753.1921 31.9870 36.9181 36 with the developed image denoising models for different D4SS 752.8882 31.8873 36.8992 36 DWT and (for different levels of DWT decomposition D1BS 724.0867 30.8230 39.0987 41 using soft thresholding technique, the following D2BS 726.9232 30.9834 38.9777 38 conclusions are derived: (a) The highest PSNR (dB) is D3BS 727.3122 31.8654 36.8764 34 obtained for first level of DWT decomposition (b) Severe D4BS 728.1129 31.8682 36.9999 34 blurring and artifacts were observed as the level of decomposition increases. (iii) Among the DWT used, C1VS 775.0098 32.2331 38.8766 39 Coiflets wavelets performed better, equally close by D4 C2VS 775.8934 32.7621 38.1234 38 and then Haar. Thus, it can be concluded that the December Issue Page 53 of 69 ISSN 2229 5208 International Journal of Computer Information Systems, Vol. 1, No. 5, 2010 performance of VisuShrink is very low when compared [15] Hangiandreou, N.J. (2003) Physics Tutorial for Residents: Topics in US: B-mode US: Basic Concepts and New Technology – to the other two. This is due to the fact that the threshold Hangiandreou, Radiographics, Vol. 23, No.4, P. 1019. does not depend on the content of the image; rather it depends on the size of image. While comparing the [16] Ibrahim, F., Osma, N.A.A., Usma, J. and Kadri, N.A. (2007) Feature extraction in Medical Ultrasonic Image, 3rd Kuala three alternatives to calculate threshold, the performance Lumpur International Conference on Biomedical Engineering, of BayesShrink in terms of image quality and IFMBE Proceedings, Springer Brlin Heidelberg, Vol.15, Pp.267- smoothness, is better when compared to SureShrink and 270. VisuShrink. Better performance can be achieved in [17] Kaur, A. and Singh, K. (2010) Speckle noise reduction by using BayesShrink if Anisotropic diffusion is combined with wavelets, National Conference on Computational Instrumentation BayesShrink, which will be considered in the next work. CSIO NCCI 2010, INDIA, Pp. 198-203. References [18] Mansourpour, M., Rajabi, M.A.A.R. and Blais, J.A. (2006) Effects and performance of speckle noise reduction filters on [1] Abdullah, H.N., Hasan, M.F. and Tawfeeq, Q.S. (2008) Speckle active radar and SAR images, Oral Presentation at the WG I/5 and noise reduction in SAR images using Double-Density Dual Tree I/6 Workshop on Topographic Mapping from Space, Ankara, DWT, Asian Journal of Information Technology, Vol. 7, No. 7, Turkey. Pp. 281-284. [19] Mastriani, M. and Giraldez, A.E. (2006) Kalman‟s Shrinkage for [2] Antoniadis, A. and Bigot, J. (2001) Wavelet Estimators in Wavelet-Based Despeckling of SAR Images, International Journal Nonparametric Regression: A Comparative Simulation Study, of Intelligent Systems and Technologies, Vol.1, No.3, Pp.190-196 Journal of Statistical Software, Vol 6, No. I, P. 06. [20] Sudha, S., Suresh, G.R. and Sukanesh, R. (2009) Comparative [3] Arivazhagan, S., Deivalakshmi, S. and Kannan, K. (2007) Study on Speckle Noise Suppression Techniques for Ultrasound Performance Analysis of Image Denoising System for different Images, International Journal of Engineering and Technology Vol. levels of Wavelet decomposition, International Journal of 1, No. 1, Pp. 1793-8236. Imaging Science and Engineering (IJISE), Vol.1,No.3, Pp. 104- [21] Tan, H.S. (2001). Denoising of Noise Speckle in radar Image. 107. [Online]. Available: http://innovexpo.itee.uq. [4] Bamber, J.C. and Daft, C. (1986) Adaptive filtering for edu.au/2001/projects/s804294/thesis.pdf reduction of speckle in ultrasonic pulse-echo images, [22] Tso, B. and Mather, P. (2009). Classification Methods for Ultrasonics, Pp. 41-44. Remotely Sensed Data (2nd ed.). CRC Press. pp. 37–38. ISBN [5] Bricker, L., Garcia, J. and Henderson, J. (2000). Ultrasound 1420090720. screening in pregnancy: a systematic review of the clinical effectiveness, cost-effectiveness and women's views". Health technology assessment (Winchester, England) 4 (16): i-vi, 1– AUTHORS PROFILE 193. [6] Bruce, A., Donoho, D. and YeGao, H. (1996) Wavelet Analysis, IEEE Spectrum, Pp.27-35. Mr. K. Karthikeyan obtained M.Sc., [7] Chang, G., Yu, B. and Vetterli, M. (2000) Adaptive Wavelet Computer Science from Nehru Memorial Thresholding for Image Denoising and Compression, IEEE College, Bharathidasan University, Trans of Image Processing, Vol. 9, No. 9, Pp. 1532-1546. Tiruchirappalli, Tamil Nadu, India, in 1997, and M.Phil., Computer Science [8] Delakis, I., Hammad, O. and Kitney, R.I.(2007) Wavelet-based from Manonmaniam Sundaranar de-noising algorithm for images acquired with parallel magnetic University, Thirunelveli, Tamil Nadu, India resonance imaging (MRI), Physics in Medicine and Biology, in 2003. He is working as Assistant Vol. 52, No.13, Pp.3741. Professor, in Department of Information Technology, Dr. SNS Rajalakshmi [9] Donoho, D.L. (1992) De-noising by soft-thresholding, IEEE College of Arts & Science, Coimbatore, Tamil Nadu, India. He is Transaction on Information Theory, Vol.41, No.3, Pp.613-627. pursing Ph.D in Image Processing. http://wwwstat.stanford.edu/~donoho/Reports/1992/denoiserelea se3.ps. [10] Donoho, D.L. and Johnstone, I.M. (1995) Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Dr. C. Chandrasekar completed his Ph.D in Statistical Association, Vol. 90, No. 432, Pp. 1200-1224. Periyar University, Salem at 2006. He worked [11] Donoho, D.L., Johnstone, I.M., Kerkyacharian, G. and Picard, D. as Head, Department of Computer (1995) Wavelet shrinkage: Asymptopia? Journal of the Royal Applications at K.S.R. College of Engineering, Statistics Society, Series B, Vol. 57, Pp. 301-369, 1995. Tiruchengode, Tamil Nadu, India from 2007 to 2008. Currently he is working as Associate [12] Federico, A. and Kaufmann, G.H. (2007) Denoising in digital Professor in the Department of Computer speckle pattern interferometry using wave atoms, Opt. Lett., Vol. Science at Periyar University, Salem, Tamil 32, Pp.1232-1234. Nadu. His research interest includes Mobile computing, Networks, Image processing and [13] Gabrea, L.A. and Gargour, C.S. (2004) Wavelet based speech Data mining. He is a senior member of ISTE and CSI. enhancement using two different threshold-based denoising algorithms , IEEE Xplore Digital Library, Canadian Conference on Electrical and Computer Engineering, Vol. 1, Pp.315-318. [14] Ghazel, M. (2004) Adaptive Fractal and Wavelet Image Denoising, Ph.D. Dissertation, Dept. Elect. Comput. Eng., University, Waterloo, Canada, 2004. December Issue Page 54 of 69 ISSN 2229 5208

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