Modified Hybrid Median Filter for Effective Speckle Reduction in Ultrasound Images

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1 Modified Hybrid Median Filter for Effective Speckle Reduction in Ultrasound Images R.VANITHAMANI 1, G.UMAMAHESWARI, M.EZHILARASI 3 1 Lecturer, Department of Biomedical Instrumentation Engineering, Avinashilingam University for Women, Coimbatore, Tamilnadu, India. Senior Lecturer, Department of ECE,PSG College of Technology, Coimbatore, Tamilnadu, India. 3 Principal-i/c, KGiSL Institute of Technology, Coimbatore, Tamilnadu, India. vanira13@yahoo.co.in, gumabhaskar@yahoo.co.in, ezhilrasi@yahoo.co.in Abstract Speckle is a granular noise that inherently exists in and degrades the quality of ultrasound images. It generally tends to reduce the resolution and contrast, thereby, to degrade the diagnostic accuracy of this modality. Speckle reduction is one of the most important processes to enhance the quality of ultrasound images. This paper proposes a statistical filter, which is a modified version of Hybrid Median Filter for speckle reduction, which computes the median of the diagonal elements and maximum of the horizontal and vertical elements in a moving window and finally the two values are compared with the central pixel and the median value of the three values will be the new pixel value. The filter is tested on phantom Ultrasound image. Effectiveness of the proposed filter is compared on the basis of Peak Signal to Noise Ratio(PSNR),Root Mean Square Error(RMSE),Structure Similarity Index(SSI), Image Quality Index(QI) and Edge Preservation Factor(EPF).The experimental results demonstrate that the proposed filter can reduce the speckle noise effectively without blurring the edges. Keywords granular noise, ultrasound image, speckle reduction, hybrid median filter, statistical filter. 1 Introduction In medical imaging modalities, ultrasound imaging has been considered to be non invasive and most prevalent diagnostic tool for imaging organs and softtissue structures of the human body. This is often preferred due to its non ionizing radiations with low cost. But this imaging has maor disadvantage of having Speckle. Speckle in ultrasound imaging is caused by the interference of energy from randomly distributed scatters, too small to be resolved by imaging system. The presence of speckle results degradation in image quality and makes it difficult for human interpretation and diagnosis. The intent of speckle reduction is to remove the distracting speckle pattern without reducing the detail in the ultrasound image. In this paper, a statistical filter is proposed for speckle reduction considering the multiplicative characteristics of speckle. Model of Speckle Noise The speckle noise model may be approximated as multiplicative and is given by f = g u + α Where f is the noisy pixel g represent the noise free pixel, u and a represent the multiplicative (1) ISSN: ISBN:

2 and additive noise respectively and are indices of the spatial locations. Because the effect of additive noise is considerably smaller compared with that of multiplicative noise (1) may be written as average of pixels in a moving window, k weighting factor ranges from 0 to 1. σ x L k = Lσ x + ( y) is a (5) f g u () Logarithmic compression is applied to the envelope detected echo signal in order to fit within the display range[1]. Logarithmic compression affects the speckle noise statistics and it becomes very close to white Gaussian noise. The logarithmic compression transforms multiplicative form in () to additive noise form as log( f ) = log( g ) + log( u ) (3 a) x = y + n (3 b) The term log( f ), which is the ultrasound image after logarithmic compression is denoted as xi, and the terms log( g ), log( u ) which are the noise free pixel and noisy component after logarithmic compression, as y and ni, respectively(3b). 3 Adaptive Speckle Filters Adaptive filters reduce speckles while preserving the edges.these filters modify the image based on statistics extracted from the local environment of each pixel. 3.1 Lee Filter The Lee filter [] utilizes the statistical distribution of the pixels in the moving window to estimate the value of pixel of interest. The filter assumes a noise distribution as in (3a).The Lee filter is based on the assumption that the mean and variance of the pixel of interest is equal to the local mean and variance of all pixels within the moving window. The formula used for the Lee filter is y = x + k ( x x ) (4) Where y( ) is the estimated noise free pixel value, xi, is the noisy pixel value in the moving window, i, are the spatial co-ordinates of the pixel value. x is where L is the Equivalent Number of Looks(ENL),which is defined as the ratio of square of mean to square of variance. 3.. Kuan Filter The Kuan filter [3] has the same form as Lee filter but with a different weighting function k and is given by σ x k = σ x + (( y) + σ x ) / L 3.3 Frost Filter The Frost filter [4] replaces the current pixel with the weighted sum of the values within nxn moving window. The weighting factors decrease with distance from the pixel of interest. The weighting factors increase for the central pixel as variance within the window increases. This filter assumes speckle noise as multiplicative and the value of current pixel is assigned as (6) y k exp( t ) x (7) = nxn α α i+ n, + n t = i + is the distance between the current pixel (n, n) and processed pixel (n + i, n +y ),α is an adaptive coefficient determined by local statistics in the moving window and k is normalization constant. It is obvious that if α is small the filter acts as a mean filter and if the value of α is large it has a tendency to preserve the original observed image, which is the feature considered in Lee and Kuan filters. 3.4 Median Filter Median filtering [7] is a nonlinear filtering method, which is used to remove the speckle noise from an Ultrasound image. It assigns to each pixel the median value of its neighbourhood. The median is calculated by first sorting all the pixel values from the surrounding neighbourhood into numerical order and then replacing the pixel being considered with the middle pixel value. This filter is relatively slow, even ISSN: ISBN:

3 with fast sorting algorithms such as quick sort. The median filter does not blur the contour of the obects. 3.5 Truncated Median Filter A technique related to median filtering is mode filtering. It accomplishes noise reduction, and also can provide for edge enhancement. The mode of the distribution of brightness values in each neighbourhood is defined as the most likely value. However, for small neighbourhoods, the mode is poorly defined. An approximation to this value can be obtained with a truncated median filter [7]. In an asymmetric distribution the mode is the highest point in the neighbourhood histogram and the median is closer to the mode than to the mean value as illustrated in fig1. For a symmetrical distribution, values are discarded from both ends and the median value does not change (it is already equal to the mode). In the truncated median method, values farthest from the mean are discarded so that the median is shifted towards the mode. The new median becomes the output value for the central pixel. Fig1.Arrangement of mode, median and mean the point to be truncated is after the mean and it is given by P P= * median max of distribution 5. Output of the truncated median filter ( ) y = median truncated vector 3.6 Hybrid Median Filter The hybrid median filter [6] is another modification of median filter. This filter is also called as corner preserving median filter is a three-step ranking operation. In a 5X5 pixel neighbourhood, pixels can be ranked in two different groups as shown in fig.. The median values of the 45 o neighbours forming an X and the 90 o neighbours forming a + are compared with the central pixel and the median value of that set is then saved as the new pixel value. The three step ranking operation does not impose a serious computational penalty as in the case of median filter. Each of the ranking operations is for a much smaller number of values than used in a square region of the same size. For example, the 5 pixel wide neighbourhood used in the examples contains either 5 (in the square neighbourhood) which must be ranked in the traditional method. In the hybrid method, each of the two groups contains only 9 pixels, and the final comparison involves only three values. Even with the additional logic and manipulation of values, the hybrid method is faster than the conventional median. This median filter overcomes the tendency of median and truncated median filters to erase lines which are narrower than the half width of the neighbourhood and to round corners Algorithm 1. Find the mean and median of the current window. Truncate the points on the side of the mean so that the median bisects the remaining points 3. If ( median < mean) then the point to be truncated is after the mean and it is given by P1 P1= * median min of distribution 4. If ( median > mean) then Fig..Diagram of neighbourhood pixels used in the hybrid median filter. As an example, for n = 5: ISSN: ISBN:

4 3.6.1 Algorithm D * R * D * D R D * R R C R R * D R D * D * R * D 1. Find the median MR of the pixels marked as R and the central pixel C in the 5x5 window. Find the median MD of the pixels marked as D and the central pixel C in the 5x5 window 3. Finally compute M M = median( MR, MD, C) 4. Filter value y = M 3.7 Modified Hybrid Median Filter This proposed filter is the modified version of the hybrid median filter explained above. It works on the sub windows similar to hybrid median filter. The max value of the 45 o neighbours forming an X and the median value of the 90 o neighbours forming a + are compared with the central pixel and the median value of that set is then saved as the new pixel value Algorithm 1. Find the median MR of the pixels marked as R and the central pixel C in the 5x5 window. Find the maximum MXD of the pixels marked as D and the central pixel C in the 5x5 window 3. Finally compute M1 M1 = median( MR, MXD, C) 4. Filter value y M1 = 3.8 Image Quality Evaluation Metrics The performance of each filter is evaluated quantitatively for phantom ultrasound image with speckle noise using the quality metrics like Root Mean Square Error(RMSE), Signal-to Noise Ratio(SNR),Peak Signal-to Noise Ratio(PSNR),Edge Preservation Factor(EPF), Structure Similarity Index(SSI) and Image Quality Index(QI). SNR: Signal to Noise Ratio (SNR) [10] compares the level of desired signal to the level of background noise. The higher the ratio, the less obtrusive the background noise is. M N ( x,, ) 1 1 i + y i= = i SNR = 10.log 10 (8) M N ( x, y, ) i 1 1 i = = i The larger SNR values correspond to good quality image. RMSE: The Root Mean square error (RMSE), which is the square root of the squared error averaged over MXN window [8]: 1 M N RMSE = ( x, y, ) (9) i 1 1 i i MN = = PSNR: Peak Signal to Noise Ratio (PSNR) is computed using [10]: PSNR = 0.log (g max / RMSE) (10) 10 where g max is the maximum intensity in the unfiltered images. The PSNR is higher for a better transformed image. QI: The universal Quality Index [11]: σ xy y x σ yσ x QI = σ xσ y ( y) + ( x) σ x + σ y (11) Where x and y represent the mean andσ x, σ y the standard deviation of original and despeckled images. σ represents the covariance between the xy original and despeckled images. ISSN: ISBN:

5 SSI: The Structural Similarity Index between two images is computed as [9]: ( x y+.55)( σ xy ) SSI = ( x + y +.55)( σ x + σ y ) (1) The SSI lies between -1 for a bad and 1 for a good similarity between the original and despeckled images. In ultrasound imaging in addition to speckle noise suppression, preservation of edges of the image also should be considered. Therefore in addition to the above performance metrics, another measure for edge preservation is also considered. More specifically, [1] has defined the parameter for edge preservation EPF. Fig3. Ultrasound Phantom image EPF: The edge preservation ability of the filter is compared by Edge Preservation Factor and is computed using [1]: ( x - x)( y - y) EPF = (13) ( x - x) ( y - y) Where x and y are the high pass filtered versions of images x and y, obtained with a 3x3 pixel standard approximation of the Laplacian operator. The larger value of EPF means more ability to preserve edges. 4 Results and Discussion Despeckling is carried out for ultrasound image with speckle noise of variance σ =0. using the standard speckle filters and the Median filter, Truncated median filter, Hybrid median filter and the proposed median filter. Figures 3and 4 show the original image and its noisy version. Simulations are carried out in MATLAB. The performances of different Despeckling schemes are compared in Table1. The obective measures for different filters are illustrated in fig.5. Fig4.Noisy image Table1. Comparison for fantom.pg FILTER RMSE SNR PSNR EPF SSI QI Lee Kuan Frost Median Truncated median Hybrid median Modified Hybrid median filter ISSN: ISBN:

6 speckle, IEEE Transactions on Acoustics Speech Signal Processing, Vol.ASSP-35,pp ,1987. [4] V.S.Frost,J.A.Stiles,K.S.Shanmugam and J.C.Holtzman, A model for radar images and its application for adaptive digital filtering of multiplicative noise, IEEE Transactions on pattern analysis and machine inelligence,vol.4,no., pp ,198. [5] Christos P. Loizou, Constantinos S. Pattichis, Speckle Filtering Algorithms and Software and Software for Ultrasound Imaging, Morgan and Claypool Publishers, 008. [6] E.R.Davies, Machine vision Theory, Algorithms, Practicalities, Elsevier, 006. [7] Mark S. Nixon, Alberto S. Aguado, Feature Extraction and Image Processing, Newnes, 00. [8] R.Gonzalez and R.Woods, Digital image processing, nd edition, prentice hall, 00. Fig.5.Filter s performance in terms of RMSE, SNR, PSNR, EPF, SSI, QI From Table 1, it can be seen that the Lee and Kuan filters perform more or less equally and better than the Frost filter. The standard median filter was the least effective among the methods compared. The performance of the hybrid median filter is better than the above mentioned filters. The truncated median filter reduces the noise and also preserves the edges. Experimental results show that the modified Hybrid median filter yielded better SNR and PSNR when compared to other filters. Other performance metrics show that while removing substantial amount of noise, it also preserves edges and details. [9] Z.Wang, A.Bovik, H,Sheik and E.Simoncell Image Quality assessment: From error measurement to structural similarity, IEEE Transaction on image processing,vol.13,no.4,pp ,april,004. [10] D.Sakrison, On the role of observer and a distortion measure in image transmission, IEEE Transaction on Communication. Vol 5,pp ,November,1977. [11]Z.Wang, A.Bovik, A Universal Quality index, IEEE Signal Processing Letters, vol.9, no.3, pp.81-84, March, 00. References: [1] V.Dutt, Statistical analysis of ultrasound echo envelope, Ph.D. dissertation, Mayo Graduate School, Rochester, [] S.Lee, Speckle analysis and smoothing of synthetic aperture radar images, Computer Graphics Image processing, vol.17, pp. 4-3, [3] D.T.Kuan, A.A.Sawchuk, T.C.Strand and P.chavel, Adaptive restoration of images with ISSN: ISBN: