ISSN: 2229371X
Dr. (Mrs). S.N Geethalakshmi^{ *1} and J.Suguna^{2}

Corresponding Author: Dr. (Mrs). S.N Geethalakshmi, Email: sngeethalakshmi@yahoo.com 
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The influence and impact of digital images on modern society is tremendous and is considered as a critical component in variety of application areas including pattern recognition, computer vision, industrial automation and healthcare industries. Medical imaging is concerned with the development of the imaging devices that help to identify different aspects of the tissue and organs based on various properties and reveal new properties of the tissue and internal structure. Examples of such devices / equipments include xray devices, CT / MRI scanners, electron microscope, etc. All these devices introduce, an unwanted signal, called noise. This paper considers a special kind of noise introduced by ultra sonographic devices is called 'speckle'. Speckle appears as interference of backscattered wave from many microscopic diffused reflection. They spread through internal organs and make it more difficult for the observer to discriminate fine detail of the images in diagnostic examinations. In this paper, hybrid models are designed for speckle removal by combining anisotropic diffusion based on 4th order PDE with the three conventional linear filters, kaun, lee and frost. Experiments were conducted with various ultrasound images. From the results, it was found that all the three hybrid methods performed denoising operation in a superior fashion and produce images that are of good visual quality.
Keywords 
Denoising, ultrasonic images, hybrid models, kaun, lee, frost 
INTRODUCTION 
Various medical imaging devices like xray, CT / MRI scanners and electron microscope produce highresolution images, which play a vital role in disease diagnosis. Out of these devices, medical sonography (ultrasonography) is an ultrasoundbased diagnostic medical imaging technique used to visualize muscles, tendons, and many internal organs, to capture their size, structure and any pathological lesions with real time tomographic images. Ultrasound has been used by sonographers to image the human body for at least 50 years and has become one of the most widely used diagnostic tools in modern medicine. The technology is relatively inexpensive and portable when compared with other techniques such as magnetic resonance imaging (MRI) and computed tomography (CT). Ultrasound is also used to visualize fetuses during routine and emergency prenatal care. Such diagnostic applications used during pregnancy are referred to as obstetric sonography. Medical sonography is used in the study of many different systems like cardiology, gastroenterology, gynecology, neurology, obstetrics, urology and cardiovascular systems (Tso and Mather, 2009). Images produced by these devices can be displayed, captured, and broadcast through a computer using a frame grabber to capture and digitize the analog video signal. The captured signal can then be postprocessed on the computer itself. Ultrasonogrpahy is widely used by practitioners as they have no longterm side effects and has the added advantage that it is nonintrusive to the patients (Hangiandreou, 2003). The device provides live images, where the operator can select the most useful section for diagnosing thus facilitating quick diagnoses (Sudha et al., 2009). However, imperfect acquisition instruments, transmission errors often distort the visual signals obtained. These distortions in ultrasound images are referred as ‘Speckle Noise’ and are considered as undesirable feature that often lead to incorrect diagnosis. 
Speckle is a complex phenomenon and it significantly degrades image quality. Speckle appears interference of backscattered wave from many microscopic diffused reflection which passing through internal organs and makes it more difficult for the observer to discriminate fine detail of the images in diagnostic examinations. Thus, it is important that to remove or reduce this noise to the maximum extent before using them (Raman and Himanshu, 2010). The goal of any speckle removal algorithm should be to enhance the corrupted images by maintaining the quality of the image. 
In this paper, the applicability of anisotropic diffusion filter, also called Perona–Malik diffusion, to speckle denoise ultrasound images is consider. Anisotropic diffusion filter is a frequently used filtering technique in digital images (Fu et al., 2006). Anisotropic diffusion is a technique aiming at reducing image noise without removing significant parts of the image content, typically edges, lines or other details that are important for the interpretation of the image (Perona and Malik 1987; 1990; Sapiro, 2001). In spite of its popularity, it faces the following problems. 
1. they cause blocky effects in images 
2. they destroy structural and spatial neighbourhood information (Pitas and Venetsanopoulos, 1990) and 
3. they are slow in reaching a convergence stage. 
Attempts made to solve these disadvantages include the development of hybrid varieties (Ling and Bovik, 2002; Rajan and Kaimal, 2006a; 2006b). Eventhough, these hybrid models produce excellent results when compared with standalone anisotropic diffusion and other filtering techniques, they come with the defect of removing finer details of an image like edges, sharp corners, thin lines (Hamza et al., 1999). 
Rajan et al. (2009) developed a hybrid method to remove noise from molecular images. The method combined anisotropic diffusion filter with 2D PDE (Partial Differential Equation) with a relaxed median filter (Wang and Zhang, 1999). This method was successful in removing molecular noise and had less blocking and artifacts in the denoised image. However, when applied to speckle noise removal, the noises were not fully removed and it had the serious flaw of slow convergence. The slow convergence is because of 2D PDE used and the failure in noise removal might be because of the relaxed median filter. The relaxed median filter, eventhough is very popular in reducing other types of noises, is not suitable for speckle noise. 
Motivated by the work of Rajan et al. (2009), the present research work proposes to combine anisotropic diffusion filter with conventional speckle noise denoising filters, namely, Kaun, Lee and Frost. Normally, the anisotropic functions are based on 2nd order PDE (Partial Differential Equation) functions. In the present research work, a fourth order PDE is used with the conventional basic anisotropic model. The combination of anisotropic diffusion function with 4th order PDE and conventional despeckling filter is proposed to reduce the speckle noise from ultrasonic images, which while denoising, preserves the edges, avoids staircase artifacts and converges in a fast manner. 
The paper is organized as below. Section 1 provided a brief overview to the topic under discussion. The second section gives an overview to Speckle noise. Section 3 explains the concepts of the techniques used in the proposed hybrid models. Section 4 presents the proposed methodology and the results of experiments conducted are presented in Section 5. Section 6 presents a short conclusion with future research directions. 
SPECKLE NOISE 
Speckle is a random, deterministic, interference pattern in an image formed with coherent radiation of a medium containing many subresolution scatterers. Speckle has a negative impact on ultrasound imaging. The presence of speckle noise in images shows a reduction of lesion detectability of approximately a factor of eight. This radical reduction in contrast resolution is responsible for the poorer effective resolution of ultrasound compared to xray and MRI. Presence of speckle noise prevents Automatic Target Recognition (ATR) and texture analysis algorithm to perform efficiently and gives the image a grainy appearance. Hence, despeckling is considered as a critical preprocessing step in medical imaging systems. Speckle noise follows a gamma distribution and is given as in Equation (1). 
where variance is aÃÂ¯ÃÂ¿ÃÂ½ÃÂ¯ÃÂ¿ÃÂ½ and g is the gray level. On an image, speckle noise (with variance 0.05) looks as shown in Figure 1a and the corresponding gamma distribution is given in Figure 1b. 
ROPOSED HYBRID FILTERS 
This paper proposes a new variant of base model, which replaces the median filter with a filter that is more suitable to remove speckle noise. The filters considered to replace median filters are (i) Kaun filter, (ii) Lee filter and (iii) Frost filter. All the three filters selected have been successfully exploited to remove speckle noise. The disadvantage of using it directly on ultrasonic images is that it produces artifacts as a side effect after removal. In order to improve anisotropic diffusion filter, traditional speckle noise removal filters and RHM model, anisotropic diffusion filter is modified to use a 4th order PDE, followed by any one of the three speckle noise removal techniques. Thus, three new hybrid models are proposed, as listed below and Figure 2 shows the methodology adopted. The techniques and algorithms used are explained in this section. 
1. 4th Order PDE based Anisotropic Diffusion Filter + Kaun Filter (ADFK Model) 
2. 4th Order PDE based Anisotropic Diffusion Filter + Lee Filter (ADFL Model) 
3. 4th Order PDE based Anisotropic Diffusion Filter + Frost Filter (ADFF Model) 
A. Anisotropic diffusion 
In anisotropic diffusion, the main motto is to encourage smoothening with in the region in preference to the smoothening across the edges. This is achieved by setting the conduction coefficient as 1 within the region and as 0 near edges, however, the main problem involved in this is the detection of the presence and absence of edges. This is done by analyzing the conduction coefficient as a function of magnitude of the gradient. A general expression (Acton et al., 2003) for anisotropic diffusion can be written by Equation (3). 
A planar image obviously satisfies (Rajan and Kaimal, 2006a), hence is a global minimum of E(u). Planar images are the only global minimum of E(u) if f ''(s) ³ 0 for all s ³ 0 because the cost functional E(u) is convex under this condition (Rajan and Kaimal, 2006b). Therefore, the evolution of Equation (9) is a process in which the image is smoothed more and more until it becomes a planar image. But in the case of second order anisotropic diffusion, ƒ”(s) may not be greater than zero for all s, which results in a stepping blocking artifact effect in the resultant image. 
D. Speckle Filters 
Several researchers have contributed techniques to resolve the despeckling problem. The main challenge is that the process of denoising is irreversible and therefore must be very careful while removing noise regions. Accidental removal of important regions should be avoidedAmong the standard filters, Lee Filter, Frost Filter (Frost et al., 1982), Median Filter and Kaun Filter (Kaun et al., 1985) have been successfully applied to the problem of speckle reduction and are discussed in this section. 
Each filter discussed in this section, has a unique reduction approach which is applied to a kernel (squaremoving window) and filtering is based on the statistical relationship that exists between the central pixel and its surrounding pixels (Figure 3). The typical size of the kernel has to be odd ranging from 3 x 3 to 33 x 33. The kernel size has to be chosen carefully, as a large size will be computationally expensive and important information might be lost due to over smoothing. Similarly, speckle reduction cannot be applied to a very small kernel. Most of the works use a 3 x 3 or 7 x 7 kernel size. 
Filtering is based on either local statistical data or on the estimation of local noise variance of the kernel. The variance thus obtained is then used to determine the amount of smoothening needed for each speckle image. The noise variance determined from the local filter window is more applicable if the intensity of an area is constant or flat while ENL is suitable if there are difficulties determining if an area of the image is flat. 
• Lee Filter 
The Lee filter uses the leastsquares approach to estimate the true signal strength of the center cell in the filter window from the measured value in that cell, the local mean brightness of all cells in the window, and a gain factor is calculated from the local variance and the noise standard deviation. The filter assumes a Gaussian (normal) distribution for the noise values, and calculates the local noise standard deviation for each filter window. The Lee filter calculation produces an output value close to the local mean for uniform areas and a value close to the original input value in higher contrast regions. Lee filters are more affective in uniform areas and can maintain edges and other fine detail. The Lee filter has no userdefined parameters. The mathematical background of the lee filter is given below. 
The Lee filter is based on the approach where smoothing is performed when the variance over an area is low or constant, otherwise, that is, if the variance is high (e.g. near edges), smoothing will not be performed. The Lee filter assumes that the speckle noise is multiplicative and can be approximated by a linear model given in Equation (12). 
EXPERIMENTAL RESULTS 
To evaluate the proposed models, eight performance metrics were used. They are, Noise Mean Value, Noise Standard Deviation, Mean Square Difference, Equivalent Number of Looks, Deflection Ratio and Figure of Merit, Peak Signal to Noise Ratio (PSNR) and Denoising time. The explanation of the first six parameters are given in Mastriani and Giraldez (2006). Four ultasound images were selected for testing the proposed models. All the proposed models were executed on a Pentium IV machine with 512 MB RAM and were developed in MATLAB 7.3. The test original images used are given in Figure 4 and 20% speckle noise was introduced in all these images. The performance of the proposed hybrid models, namely, ADFK, ADFL and ADFF models were judged by comparing the result with the conventional models. The models chosen for comparison are median filter, Kaun Filter, Lee Filter, Frost Filter, SRAD filter and SRAD + Median Filter (Base Model). 
A. Noise Mean Value 
The Noise Mean Value was calculated for all the test images, before and after filtering, for all filters and the results obtained are shown in Table 1. 
From the Noise Mean Values projected in Table 1, it is clear that all the three proposed hybrid models produce better results than the conventional models. To evaluate the overall model performance, the average value of the four models were calculated. From the Table, it can be seen that among the ten models, ADFF produce better results in all the four images. This was followed by ADFL and ADFK. 
B. Noise Standard Deviation (NSD) 
The noise standard deviation obtained for the four test noisy images are projected in Table 2. 
From the results, it could be seen that the ADFF filter again outperforms all the other proposed models and the conventional models. This result is at par with the results of Table 2, which shows that the NSD results are consistent. 
C. Mean Square Difference (MSD) 
The Mean Square Difference (MSD) obtained for all the three proposed models and the selected six conventional filter models are shown in Table 3. 
The high PSNR obtained gives the understanding that the visual quality of the denoised image is good. According to Venkatesan et al. (2008), an improved denoising algorithm is recognized by a high PSNR or a lower MSE. In agreement with this, the results of the proposed systems with high PSNR prove that they are an improved version over existing methods. Similarly, according to the report of Schneier and AbdelMottaleb (1996), a PSNR value in the range 3040 indicates that the resultant image is a very good match to the original image. In accordance with this report, the results of all the three the proposed hybrid algorithms produce PSNR values in the range 4046dB proving that it is an enhanced version when compared with the conventional algorithms. 
H. Despeckling Time 
Table 8 shows the time taken by the proposed and conventional filters to perform the denoising operation. 
While considering the execution time, the ADFF model was the quickest in despeckling the noisy image, which was followed by ADFK and ADFL. This clearly shows that the introduction of 4th order PDE based anisotropic diffusion function combined with knau, lee and frost filters converges quickly, which consequently speeds up the despeckling process. 
According to Müldner et al. (2005), PSNR and speed are the two most important performance factors of any denoising algorithm. From the results, it is evident that the speed of the proposed denoising algorithms are faster when compared to the standard algorithms and therefore makes it an attractive option for several advanced applications in the field of medical imaging. 
The visual comparison of the denoised image produced by the various conventional and proposed filters is shown in Figure 5 for image UC 1. Similar quality was observed with all other test images also. 
CONCLUSION 
Thus, the various results of the experiments conducted clearly indicate that the images produced by the proposed despeckling algorithm are of good visual quality and therefore can be applied to most of the image medical processing systems. The three hybrid models can be combined with wavelet shrinkage function to improve the convergence time. The three shrinkage functions, VisuShrink, BayesShrink and PureShrink can be applied and the performance can be compared. The present work focused on producing despeckling algorithms which reduces the noise from the noisy image. The work has not considered the memory efficiency and computation complexity, which can be analyzed in future. 
References 
