**1. Introduction**

The use of ultrasound imaging in medical diagnosis is well established because of its noninvasive nature, low cost, capability of forming real time imaging and continuing improvement in image quality. However, it suffers from a number of shortcomings and these include: acquisition noise from the equipment, ambient noise from the environment, the presence of background tissue, other organs and anatomical influences such as body fat, and breathing motion. Therefore, noise reduction is very important, as various types of noise generated limits the effectiveness of medical image diagnosis.

Ultrasound is a sound wave with a frequency that exceeds 20 kHz. It transports energy and propagates through several means as a pulsating pressure wave [1]. It is described by a number of wave parameters such as pressure density, propagation direction, and particle displace‐ ment. If the particle displacement is parallel to the propagation direction, then the wave is called a longitudinal or compression wave. If the particle displacement is perpendicular to the propagation direction, it is a shear or transverse wave. The interaction of ultrasound waves with tissue is subject to the laws of geometrical optics. It includes reflection, refraction, scattering, diffraction, interference, and absorption. Except from interference, all other interactions reduce the intensity of the ultrasound beam.

Ultrasound technique is mainly based on measuring the echoes transmitted back from a medium when sending an ultrasound wave to it. In the echo impulse ultrasound technique, the ultrasound wave interacts with tissue and some of the transmitted energy returns to the transducer to be detected by the instrument [2]. Further, the reflected waves are picked up by the transducer probe and relayed to the machine. The machine calculates the distance from the transducer probe to the tissue or organ (boundaries) using the speed of sound in tissue (1,540 m/s) and the time of the each echo's return ( millionths of a second). The machine displays

© 2013 Hiremath et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Hiremath et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

the distances and intensities of the echoes on the screen, forming a two dimensional image. Superficial structures such as muscles, tendons, testes, breast and the neonatal brain are imaged at a higher frequency (7- 18 MHz), which provides better axial and lateral resolution. Deeper structures such as liver and kidney are imaged at a lower frequency 1-6 MHz with lower axial and lateral resolution but greater penetration.

The usefulness of ultrasound imaging is degraded by the presence of signal dependent noise known as speckle. Speckle noise is multiplicative in nature. This type of noise is an inherent property of medical ultrasound imaging and because of this noise the image resolution and contrast become reduced, which effects the diagnostic value of this imaging modality [3]. So, speckle noise reduction is an essential pre processing step, whenever ultrasound imaging is used for medical imaging. Therefore, image despeckling is a very important task, and should be filtered out [4-6], without affecting important features of the image.

In ultrasound images, the noise content is multiplicative and non Gaussian. Such noise is generally more difficult to remove than additive noise, because the intensity of the noise varies with the image intensity. A model of multiplicative noise is given by

$$y\_{ij} = \, \mathbf{X}\_{ij} \mathbf{n}\_i \tag{1}$$

*Variance*: It determines the average dispersion of the speckle in the image. A lower var‐ iance gives a cleaner image as more speckles are reduced. The formula for calculating the

*Mean Square Error*: The MSE measures the quality change between the original image (X) and

<sup>2</sup> N 1

The MSE has been widely used to quantify image quality and, when used alone, it does not correlate strongly enough with perceptual quality. It should be used, therefore, together with

*Signal to Noise Ratio*: The SNR compares the level of desired signal to the level of background noise. The higher the ratio, the less obtrusive the background noise is. It is expressed in decibels

> 2 2 e

> > 2

<sup>σ</sup> SNR 10 log10 <sup>σ</sup> æ ö ç ÷ <sup>=</sup> ç ÷ è ø

<sup>2</sup> <sup>S</sup> PSNR 10 log10 MSE æ ö <sup>=</sup> ç ÷

where S is the maximum intensity in the original image. The PSNR is higher for a good quality image and lower for a poor quality image. It measures image fidelity, that is, how closely the

*Correlation Coefficient*: It represents the strength and direction of a linear relationship between two variates. The best known is the Pearson product moment correlation coefficient, which is obtained by dividing the covariance of the two variables by the product of their standard

is the variance of the original image and σ<sup>e</sup>

between the original and denoised image i.e. |X - Y|).

Peak Signal-to-Noise Ratio: The PSNR is computed as

transformed image resembles the original image.

deviations, and it is given by

<sup>2</sup> ,j 0 <sup>1</sup> M SE X Y <sup>N</sup> ij ij <sup>i</sup> - =

æ ö <sup>=</sup> <sup>å</sup> ç ÷ - è ø (3)

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203

<sup>ö</sup> <sup>æ</sup> <sup>=</sup> <sup>å</sup> <sup>ç</sup> - <sup>÷</sup> è ø (4)

is the variance of error (Difference

è ø (6)

(5)

N 1 <sup>2</sup> <sup>2</sup> <sup>2</sup> ,j 0 1 σ XX <sup>N</sup> ij <sup>i</sup> - =

where X¯ is the mean intensity value of the image X of size N×N.

denoised image (Y) of size N×N. It is given by

other quality metrics and visual perception.

variance is

(dB) as

where, σ<sup>2</sup>

where the speckle image yij is the product of the original image Xij, and the non-Gaussian noise nij. The indices i, j represent the spatial position over the image. In most applications involving multiplicative noise, the noise content is assumed to be stationary with unitary mean and unknown noise variance σ<sup>2</sup> . To convert multiplicative noise into an additive noise, as given in the Eq.(2), a logarithmic transformation is applied to the speckle image yij [7]. The noise component nij is then approximated as an additive zero mean gaussian noise.

$$\ln \mathbf{y}\_{\text{ij}} = \ln \mathcal{X}\_{\text{ij}} + \ln \mathbf{n}\_{\text{ij}} \tag{2}$$

The Discrete Wavelet Transform (DWT) is then applied to ln yij and the wavelet transformed image is subjected to thresholding. After applying the inverse DWT, the processed image is subjected to an exponential transformation, which is the inverse logarithmic operation,that yields a denoised image.

#### **1.1. Image quality assessment**

Image quality is important when evaluating or segmenting ultrasound images, where speckle obscures subtle details in the image [8]. In a recent study [9] it is shown that speckle reduction improves the visual perception of the expert in the assessment of ultrasound imaging of the human organs. The statistical parameters like Signal to Noise Ratio (SNR), Correlation Coefficient (CC), variance, Mean Square Error (MSE) and Peak Signal to Noise Ratio (PSNR) for image quality assessment are described below. The following metrics are calculated using the original image X and the despeckled image Y.

*Variance*: It determines the average dispersion of the speckle in the image. A lower var‐ iance gives a cleaner image as more speckles are reduced. The formula for calculating the variance is

$$\sigma^2 = \frac{1}{\mathbf{N}^2} \sum\_{\mathbf{i}\_\emptyset=0}^{N-1} \left( \mathbf{X}\_{\mathbf{i}\mathbf{j}} - \mathbf{X} \right)^2 \tag{3}$$

where X¯ is the mean intensity value of the image X of size N×N.

the distances and intensities of the echoes on the screen, forming a two dimensional image. Superficial structures such as muscles, tendons, testes, breast and the neonatal brain are imaged at a higher frequency (7- 18 MHz), which provides better axial and lateral resolution. Deeper structures such as liver and kidney are imaged at a lower frequency 1-6 MHz with

The usefulness of ultrasound imaging is degraded by the presence of signal dependent noise known as speckle. Speckle noise is multiplicative in nature. This type of noise is an inherent property of medical ultrasound imaging and because of this noise the image resolution and contrast become reduced, which effects the diagnostic value of this imaging modality [3]. So, speckle noise reduction is an essential pre processing step, whenever ultrasound imaging is used for medical imaging. Therefore, image despeckling is a very important task, and should

In ultrasound images, the noise content is multiplicative and non Gaussian. Such noise is generally more difficult to remove than additive noise, because the intensity of the noise varies

where the speckle image yij is the product of the original image Xij, and the non-Gaussian noise nij. The indices i, j represent the spatial position over the image. In most applications involving multiplicative noise, the noise content is assumed to be stationary with unitary mean and

the Eq.(2), a logarithmic transformation is applied to the speckle image yij [7]. The noise

The Discrete Wavelet Transform (DWT) is then applied to ln yij and the wavelet transformed image is subjected to thresholding. After applying the inverse DWT, the processed image is subjected to an exponential transformation, which is the inverse logarithmic operation,that

Image quality is important when evaluating or segmenting ultrasound images, where speckle obscures subtle details in the image [8]. In a recent study [9] it is shown that speckle reduction improves the visual perception of the expert in the assessment of ultrasound imaging of the human organs. The statistical parameters like Signal to Noise Ratio (SNR), Correlation Coefficient (CC), variance, Mean Square Error (MSE) and Peak Signal to Noise Ratio (PSNR) for image quality assessment are described below. The following metrics are calculated using

component nij is then approximated as an additive zero mean gaussian noise.

*ij ij i y Xn* = (1)

. To convert multiplicative noise into an additive noise, as given in

ij ij ij ln y = ln X + ln n (2)

lower axial and lateral resolution but greater penetration.

202 Advancements and Breakthroughs in Ultrasound Imaging

be filtered out [4-6], without affecting important features of the image.

with the image intensity. A model of multiplicative noise is given by

unknown noise variance σ<sup>2</sup>

yields a denoised image.

**1.1. Image quality assessment**

the original image X and the despeckled image Y.

*Mean Square Error*: The MSE measures the quality change between the original image (X) and denoised image (Y) of size N×N. It is given by

$$\text{MSE} = \frac{1}{\text{N}^2} \sum\_{\mathbf{i}, \mathbf{j}=0}^{\text{N}-1} \left( \mathbf{X}\_{\mathbf{i}\mathbf{j}} - \mathbf{Y}\_{\mathbf{i}\mathbf{j}} \right)^2 \tag{4}$$

The MSE has been widely used to quantify image quality and, when used alone, it does not correlate strongly enough with perceptual quality. It should be used, therefore, together with other quality metrics and visual perception.

*Signal to Noise Ratio*: The SNR compares the level of desired signal to the level of background noise. The higher the ratio, the less obtrusive the background noise is. It is expressed in decibels (dB) as

$$\text{SNR} = 10 \log\_{10} \left( \frac{\sigma^2}{\sigma\_\circ^2} \right) \tag{5}$$

where, σ<sup>2</sup> is the variance of the original image and σ<sup>e</sup> 2 is the variance of error (Difference between the original and denoised image i.e. |X - Y|).

Peak Signal-to-Noise Ratio: The PSNR is computed as

$$\text{PSNR} = 10 \log\_{10} \left( \frac{\text{S}^2}{\text{MSE}} \right) \tag{6}$$

where S is the maximum intensity in the original image. The PSNR is higher for a good quality image and lower for a poor quality image. It measures image fidelity, that is, how closely the transformed image resembles the original image.

*Correlation Coefficient*: It represents the strength and direction of a linear relationship between two variates. The best known is the Pearson product moment correlation coefficient, which is obtained by dividing the covariance of the two variables by the product of their standard deviations, and it is given by

( ) ( ) 2 ij ij ij ij 2 2 2 2 2 2 ij ij ij ij N XY X Y CC N X- X N Y Y å åå - = åå å - (7)

Often a 3× 3 square kernel is used. If the coefficients of the mask sum up to one, then the average brightness of the image is not changed. If the coefficients sum to zero, the average brightness

The common speckle filters such as Lee, Kuan and Wiener filters are considered for the study. The brief definition and mathematical description of the standard spatial filters are discussed

The Lee filter [12] is based on the approach that the smoothing is performed on the area having low variance. However, smoothing will not be performed on area of high variance, which is near edges. The Lee filter assumes that the image can be approximated by a linear model

where Yij is the gray scale value of the pixel at ( i, j) after filtering. If there is no smoothing, the filter will output, only the mean intensity value K¯ of the kernel K, otherwise, the difference between the centre pixel C and K¯ is calculated and multiplied with a weighting function W

where MxM is the size of the kernel and Kuv is the pixel value within the kernel at indices u and v, K¯ is the mean intensity value of kernel. The parameter <sup>σ</sup><sup>2</sup> is the variance of the image X, which is given by the Eq.(3). The main disadvantage of Lee filter is that it tends to ignore

The Kuan filter [13] is a generalization of the Lee filter. The Kuan filter converts the multipli‐ cative model of speckle into an additive linear form. However, it is based on the equivalent number of looks (ENL), which is computed from an ultrasound image to determine a different

)

W= (1 - Cu / Ci

W= <sup>σ</sup><sup>k</sup> 2 (σ<sup>k</sup>

=K¯ <sup>+</sup> W\*(C - K¯) (8)

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<sup>2</sup> <sup>+</sup> <sup>σ</sup>2) (9)

(Kuv - K¯) <sup>2</sup> (10)

(1 <sup>+</sup> Cu) . (11)

<sup>2</sup> is the variance of the pixel values within the kernel given

Yij

σk <sup>2</sup> <sup>=</sup> <sup>1</sup> <sup>M</sup><sup>2</sup> ∑ u,v=0 M-1

speckle noise in the areas closest to edges and lines.

weighting function W given by the Eq.(11):

is lost, and it returns a dark image.

below:

*Lee filter:*

represented by Eq.(8)

given in Eq.(9) :

by the Eq. (10):

*Kuan filter:*

and then summed with K¯, where <sup>σ</sup><sup>k</sup>

where the summations are done over both the indices i and j from 0 to N-1. If the correlation coefficient is near to +1, then there exists stronger positive correlation between the original image and despeckled image.

*Computational time*: The computational time (Tc) of a filter is defined as the time taken by a digital computing platform to execute the filtering algorithm when no other software, except the operating system, runs on it. Normally, Tc depends on the computing system's clock time period. But, in addition to the clock period, it depends on the memory size, the input data size, and the memory access time, etc. The computational time taken by a filter should be low for online and real time image processing applications. Hence, a filter with lower Tc is better than a filter having higher Tc value while all other performance measures remain identical.

#### **1.2. Image data set**

For the purpose of experimentation, a medical ultrasound image database is prepared in consultation with a medical expert for the present study. The images are acquired using the instrument GE LOGIQ 3 Expert system with 5 MHz transducer frequency, in JPEG format. The data set consists of 70 ultrasound images of size 512x512, of kidney and liver.

In the present Chapter, the aim of the study is to address, novel issues related to despeckling medical ultrasound images. It is envisaged that the results of this investigation would be used as a pre processing step for effective image segmentation or image registration techniques in other applications also.

The remaining part of this Chapter is organised into five sections. The section 2 deals with common speckle filters. The section 3 examines wavelet transform methods, while the section 4 investigates contourlet transform methods. The section 5 describes the Gaussian model of speckle noise. Finally, the section 6 gives the conclusions.
