Speckle noise reduction from medical ultrasound images using wavelet thresh

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

283

SPECKLE NOISE REDUCTION FROM MEDICAL ULTRASOUND IMAGES

USING WAVELET THRESHOLDING AND ANISOTROPIC DIFFUSION

METHOD

Ratil Hasnat Ashique1, Md Imrul Kayes

2, M T Hasan Amin

3, Badrun Naher Lia

4

1Primeasia University, Department of EEE, 12, Kamal Atartuk Avenue, Banani, Dhaka

2International Islamic University Chittagong, Department of CSE, Chittagong 3University of Surrey, Department of Electronics Engineering, Surrey, UK

4Primeasia 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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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-


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


50). Intensity values of each pixel in the window are sorted in an array. The pixel in the center of the


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



moothing at the image edges. This function is called diffusion coefficient. The diffusion coefficient


region smoothing. To smooth image on a continuous domain:

onal Journal of Electronics and Communication Engineering & Technology (IJECET),

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xel in the center of the


Median filtering is shown

efficient nonlinear technique for simultaneously performing



moothing at the image edges. This function is called diffusion coefficient. The diffusion coefficient




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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.



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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


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)


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


PROPOSED FILTER


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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Speckle noise reduction from medical ultrasound images using wavelet thresh

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