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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
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 ( 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.

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                                                                                  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.
         S' = FS                                       (2)                               (i) Shrinkage Rule – Calculate
          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
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
filters are able to reduce speckle while preserving the           1       2
data. However, all these uses a lossy approach, as all            3       4
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
                                                                                    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 )
                                                                              i 0
                                                                                  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)
      median (| g j1, 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
         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
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 ( x , y)                              (15)
SureShrink Thresholding                                                          n x , y 1

          A threshold chooser based on Stein‟s Unbiased                    s  max( 2  2 ,0)                                (16)
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
computed from Equation (4.9), and n is the size of the
image. SureShrink follows the soft thresholding rule.                         Haar        I, II, III, IV  VisuShrink
The thresholding employed here is adaptive, i.e., a

   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)
                                     SureShrink                        MSD indicates average square difference of the
                                                              pixels throughout the image between the original image
                                                              (with speckle) (Is) and denoised image (Id ). A lower
                                                              MSD indicates a smaller difference between the original
                                                  H2BS,       (with speckle) and despeckled image. This means that
                                                  H3BS,       there is a significant filter performance. Nevertheless, it
                                                              is necessary to be very careful with the edges. The
                                                  D1VS,       formula for the MSD calculation is given in Equation
                                                  D2VS,       (17)
                                                  D4VS                   (I s (r, c)  I d (r, c))

                                                  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)
                                                  D2BS,       NV determines the contents of the speckle in the image.
                                    BayesShrink               A lower variance gives a “cleaner” image as more
                                                  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)
                                                  C3VS,                 NMV 
                                                                                      r ,c
                                                  C4VS                                   R *C
                                                  C1SS,                                                    2        (19)
                                                                                (I d (r, c)  NMV)
   Coiflets      I, II, III, IV      SureShrink                         NV 
                                                                               r, c
                                                  C3SS,                                      R *C
                                                  C1BS,                 NSD            NV                          (20)
                                                              where I is the image, r and c are the number of rows and
                                                              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 )]
                                                     (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.

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                                                                                                  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
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                                                                                                 Technology, Dr. SNS Rajalakshmi
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     32, Pp.1232-1234.                                                                            Nadu. His research interest includes Mobile
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[14] Ghazel, M. (2004) Adaptive Fractal and Wavelet Image
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     University, Waterloo, Canada, 2004.

      December Issue                                              Page 54 of 69                                          ISSN 2229 5208

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