1. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME
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SPECKLE NOISE REDUCTION FROM MEDICAL ULTRASOUND IMAGES
USING WAVELET THRESHOLDING AND ANISOTROPIC DIFFUSION
METHOD
Ratil Hasnat Ashique1
, Md Imrul Kayes2
, M T Hasan Amin3
, Badrun Naher Lia4
1
Primeasia University, Department of EEE, 12, Kamal Atartuk Avenue, Banani, Dhaka
2
International Islamic University Chittagong, Department of CSE, Chittagong
3
University of Surrey, Department of Electronics Engineering, Surrey, UK
4
Primeasia University, Department of EEE, 12, Kamal Atartuk Avenue, Banani, Dhaka
ABSTRACT
Medical Images are very often corrupted by various types of noise including speckle noise,
salt and pepper noise etc. This corruption of noise is introduced to the original image during image
acquisition and transmission. The various image denoising techniques that are proposed from time to
time are offering denoising techniques preserving the original image features. The denoising is so
important because ultrasound imaging today has gained wide acceptance due to its safety, easy
imaging procedure, low cost and adaptability. However the main shortcomings of this process is poor
quality of images which is further degraded due to the presence of speckle noise and other types of
noise. Hence it has become vital to remove noise while preserving important datails and features of
the image. This paper will introduce a unique method to speckle noise filtering using median filters,
wavelet and SRAD filters.
Keyword: Ultrasound Image, Ultrasonography, Speckle Noise, Wavelet, Hard Threshold, Soft
threshold, SNR, PSNR, MSE, RMSE, Median filter, SRAD filter.
1. INTRODUCTION
Compared to other medical imaging techniques ultrasound images suffers from lower image
contrast, low Signal to noise ratio, signal dropouts, shadowing of structures, variable intensity
problem etc. Moreover very often they contain high noise contents against poor contrast. This
ultimately results in blurred image, missing edge points, fake edge points etc. Hence due to complex
and changing shapes it becomes difficult to obtain a correct edge map which is vital for diagnosis
purpose. Speckle noise comes up as a result of interference between multiple scattering beams and
main reflected signal. Speckle noise is a granular noise that inherently exists in and degrades the
quality of the images. Generally it is found in ultrasound image and radar image. This noise is, in
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ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME
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fact, caused by errors in data transmission. The corrupted pixels are either set to the maximum value,
which is something like a snow in image or have single bits flipped over. This kind of noise affects
the ultrasound images. Speckle noise has the characteristic of multiplicative noise. Speckle noise
follows a gamma distribution and is given as
Where, α is variance and g is the gray level.
2. NECESSITY TO REMOVE SPECKLE NOISE
As most prevalent artifact in ultrasound image which makes object detection and recognition
more difficult, reduction of speckle directly improves the value of the sonogram.
Because Ultrasound Images have very little contrast, edge detection is essential to object
detection. Ultrasounds depend more heavily on edge detection than other medical imaging
modalities. Speckle noise can distort or hide edges making object detection less reliable. Objects
such as tumors or birth defects can go undetected and thus untreated
3. SPECKLE NOISE STATISTICS
The Rayleigh density function, and its extension, the Rice density function, provide a good
starting point for the model for the statistics of the envelope signal. The Rayleigh density function
provides a good model for the backscattered echo signals when the scatterer density is very large
(>10 scatterers per resolution cell). This model has been used extensively for such fully formed
speckle situation. Similarly, the Rice model provides a good model for the presence of coherent
backscatter.
4. REMOVING SPECKLE NOISE
To develop a despeckling algorithm to filter out speckle noise we have know the
mathematical model of the speckle noise .The simplified model can be described as follows:
As we know speckle noise is a multiplicative noise, the logarithm of the noisy image is taken to
convert the noise function to an additive one .Hence for a possible imaging let
F1(m,n)=F2(m,n)*N(m,n) --------------------------(1)
where F1,F2 and N are the noisy image , original image without noise and noise function
respectively.By taking log on both sides eqn (1) becomes
Log{F1(m,n)}=Log{F2(m,n)}+Log{N(m,n)}---(2)
In eqn (2) as we observe the noise becomes an additive noise which is processed by various noise
removing filters. Denoised Image is obtained by taking the exponential of the image matrix.
5. MEDIAN FILTER
Median filter is a nonlinear spatial filter which is good at removing pulse and spike noise.
The filtering process is described here-

3. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 –
Here a NxN window is centered around each pixel. Generally N is a small odd number (~5 to
50). Intensity values of each pixel in the window are sorted in an array. The pi
window is replaced in the final image with the median value of the pixels in the window. It is simple
filter to implement and good at removing “salt and pepper” type noise.
graphically below
Here following thing are done
a. Window centers on target pixel.
b. Intensity values are ordered for each pixel in the w
c. Mean Value is selected for new image
6. ANISOTROPIC DIFFUSION FILTERS
Anisotropic diffusion is an
contrast enhancement and noise reduction. It smoothes homogeneous image regions and retains
image edges. The main concept of anisotropic diffusion is the introduction of a function that inhabits
smoothing at the image edges. This function is called diffusion coefficient. The diffusion coefficient
is chosen to vary spatially in such a way to encourage intra region smoothing in preference to inter
region smoothing. To smooth image on a continuous dom
onal Journal of Electronics and Communication Engineering & Technology (IJECET),
– 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME
285
Here a NxN window is centered around each pixel. Generally N is a small odd number (~5 to
50). Intensity values of each pixel in the window are sorted in an array. The pixel in the center of the
window is replaced in the final image with the median value of the pixels in the window. It is simple
filter to implement and good at removing “salt and pepper” type noise. Median filtering is shown
e ordered for each pixel in the window.
ean Value is selected for new image.
ANISOTROPIC DIFFUSION FILTERS
Anisotropic diffusion is an efficient nonlinear technique for simultaneously performing
contrast enhancement and noise reduction. It smoothes homogeneous image regions and retains
image edges. The main concept of anisotropic diffusion is the introduction of a function that inhabits
moothing at the image edges. This function is called diffusion coefficient. The diffusion coefficient
is chosen to vary spatially in such a way to encourage intra region smoothing in preference to inter
region smoothing. To smooth image on a continuous domain:
onal Journal of Electronics and Communication Engineering & Technology (IJECET),
August (2013), © IAEME
Here a NxN window is centered around each pixel. Generally N is a small odd number (~5 to
xel in the center of the
window is replaced in the final image with the median value of the pixels in the window. It is simple
Median filtering is shown
efficient nonlinear technique for simultaneously performing
contrast enhancement and noise reduction. It smoothes homogeneous image regions and retains
image edges. The main concept of anisotropic diffusion is the introduction of a function that inhabits
moothing at the image edges. This function is called diffusion coefficient. The diffusion coefficient
is chosen to vary spatially in such a way to encourage intra region smoothing in preference to inter

4. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME
286
Where ∇ is the gradient operator, div is the divergence operator, || is the magnitude, c(x) is the
diffusion coefficient, and I0 is the initial image. For c(x), they have two coefficients options:
Where k is the edge magnitude parameter. c(x) is the conduct coefficient along four directions. In
practical design, the diffusion coefficient c(∇I ) is anisotropic, and thus it’s called anisotropic
diffusion. The option 1 of the diffusion coefficient favors high contrast edges over low contrast ones.
The option 2 of the diffusion coefficient favors wide regions over smaller ones. The edge magnitude
parameter k controls conduction as a function of gradient. If k is low, then small intensity gradients
are able to block conduction and hence diffusion across step edges. A large value of k can overcome
the small intensity gradient barrels and reduces the influence of intensity gradients on conduction.
Usually k ~ [20,100]. This method can be iteratively applied to the output image, and the iteration
equation is:
where I (n) is the output image after n iterations. λ is the diffusion conducting speed, usually we set
λ<=0.25.
7. WAVELET BASED DENOISING
Wavelet transform(WT) is another transformation method like Fourier transform(FT) except
that time and frequency information is obtained simultaneously in the later. FT has the drawback that
it cannot provide time information of the frequency bands which is specially important in case of non
stationary signals. Though STFT although provides time frequency information of the signal ,it
suffers from resolution problem. WT removes this resolution problem also. As most of the practical
signals are non stationary type , it is crystal clear that WT has higher preference in signal analysis.
The continuous wavelet transform is given by
Xw(a,b)=(1/√a)∫[h*{(t-b)/a}x(t)]
Where h(t) is the wavelet basis function and x(t) is the original signal.
Wavelet techniques are widely used for image denoising and image compression. The
wavelet denoising method decomposes the signal image into wavelet basis and shrink the wavelet
coefficients to remove speckle. At every level the coefficients are run through soft thresholding
process. After thresholding inverse wavelet transform is performed to reconstruct the image.
In short,
• Decomposition: A wavelet chosen with level N. The wavelet decomposition of the signal is
computed at level N.
• Threshold detail coefficients: For each level from 1 to N, a threshold selected and soft
thresholding applied to the detail coefficients.
• Reconstruction: Wavelet reconstruction using the original approximation coefficients of level
N and the modified detail coefficients of levels from 1 to N is performed.

5. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME
287
8. PROPOSED METHOD
In our method we first produce artificial speckle noise which is then combined with synthetic
ultrasound image to produce noisy test image. At first, denoising is performed using median filter to
move long tailed noise such as negative exponential , salt and pepper noise ,spike or pulse noises etc.
This of course causes minimum blurring to the image. The process is specially useful if the image
contains strong unusual spikes.
Secondly, the noisy image is then processed by Wavelet denoising by passing the noisy
signal through a wavelet filter and soft thresholding the detail coefficients for speckle removal.
At the third step ,SRAD2 filter is used to enhance the contrast of the image, smoothing
homogeneous regions and to retain image edges.
The whole process can be shown using block diagram as follows:
Figure 1: Block Diagram
Finally MSE, RMSE, SNR, PSNR are calculated the proposed method and compared with
other types of filters. The process is done for three test images. Window size remains fixed 3×3.
9. SIMULATION
Here we have used MATLAB as a simulation software .The filters codes are written and
image processing toolbox is also used to enhance the simulation.
10. COMPARISON PARAMETERS
To determine the image enhancement we have measured The Root Mean Square Error
(RMSE), signal-to-Noise Ratio (SNR), and Peak Signal to Noise Ratio (PSNR) of the noisy image
The RMSE, SNR, and PSNR are provided below.
Synthetic Ultrasound image +Speckle noise
Noisy Image
SRAD1 filtering
Median Filtering
WT Denoising
Original Image without noise
Process flow
direction

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Figure 2: Measurement Parameters
Where,
f= original image function
F=enhanced image function
σ=variance of the original image
σe=variance of the enhanced image
i,j=position of pixel value of image matrix
11. COMPARISON TABLE
TEST IMAGE# 1
Parameter Lee Median SRAD2 Proposed
MSE 51.4582 58.9049 94.2244 60.5280
RMSE 7.1734 7.6750 9.7069 6.9737
SNR 12.8863 17.2534 15.7889 15.6327
PSNR 31.0163 30.4293 28.3892 29.0713
TEST IMAGE# 2
TEST IMAGE# 3
Parameter Lee Median SRAD2 Proposed
MSE 64.7943 52.6241 96.9385 62.9299
RMSE 8.0495 7.2542 9.8457 7.8399
SNR 11.8560 16.7346 14.3236 11.8973
PSNR 30.0154 30.9190 28.2658 22.5017
Statistical
Measurement
Formula
MSE ∑(f(i,j)-F(i,j)^2)/MN
RMSE √(∑(f(i,j)-F(i,j))^2)/MN)
SNR 10*log((σ^2)/(σ(e)^2)
PSNR 20*log10(255/RMSE)
Parameter Lee Median SRAD2 Proposed
MSE 59.7539 36.5858 85.7866 51.9390
RMSE 7.7301 6.0486 9.2621 6.2069
SNR 9.9015 16.1473 13.0639 12.1305
PSNR 30.3671 32.4977 28.7966 29.9759

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step3:enhanced image with proposed filtersalt peepered+speckled image
step3:enhanced image with proposed filterspeckled image salt peepered+speckled image
step3:enhanced image with proposed filtersalt peepered+speckled imagespeckled image
TEST IMAGE 1 NOISY IMAGE DENOISED WITH
PROPOSED FILTER
TEST IMAGE 2 NOISY IMAGE DENOISED WITH
PROPOSED FILTER
TEST IMAGE 3 NOISY IMAGE DENOISED WITH
PROPOSED FILTER
12. CONCLUSION
The tested result shows that the proposed multilevel filtering technique provides better
resolution, edge preservation with improved SNR compared with other linear and nonlinear filtering
techniques.
Moreover, signal to noise ratio(SNR),mean square error(MSE) are significantly improved by
using the proposed filtering method.
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ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME
290
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