A ROBUST LONE DIAGONAL SORTING ALGORITHM FOR DENOISING OF IMAGES WITH SALT AND PEPPER NOISE

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1 International Journal of Computational Intelligence & Telecommunication Systems, 2(1), 2011, pp A ROBUST LONE DIAGONAL SORTING ALGORITHM FOR DENOISING OF IMAGES WITH SALT AND PEPPER NOISE Rajamani. A 1, Krishnaveni. V 2, Wassim Ferose. H 3 and Gokul Prasath. R 4 Dept.of ECE, PSG Polytechnic College, Coimbatore , Tamilnadu, India 1 hod@dec.psgtech.ac.in, 2 vk@ece.psgtech.ac.in Abstract: A new and highly efficient algorithm for denoising an image with salt and pepper noise is proposed. Existing standard algorithms such as Standard Median Filter (SMF), Weighted Median Filter (WMF), etc exhibit poor performance at higher noise densities. The proposed lone diagonal sorting algorithm uses diagonal sorting alone for denoising of salt and pepper noise and is compared with the above algorithms. The results are promising at all noise densities. The new algorithm has lower computational time and the obtained results prove that it has better visual appearance and quantitative measures at noise densities ranging up to 90%. Keywords: Median filter, Lone Diagonal Sorting, Salt and pepper noise, Peak signal to noise ratio, Mean square error. I. INTRODUCTION The digital images when being acquired by defective sensors or transmitted through erroneous radio channels take into their true signal positions unreliable information. These noisy signals when exist as maximum or minimum magnitudes relative to the surrounding signals are called the impulses [1], [2]. So impulse noise removal is a very important pre-processing step to go through the subsequent stages of image processing applications [3]. The initial attempt made towards impulse noise removal by the linear operators tend to blur sharp edges, destroy lines and other fine image details [4], [5] of the impulse corrupted digital image due to their inability to simultaneously eradicate noise and preserve high frequency information. The nonlinear filters were found capable of dealing the impulse characteristics and the foremost role was taken by the non-linear Median Filter [6]. The best-known and most widely used nonlinear digital filters, based on order statistics are median filters. Median filters are known for their capability to remove impulse noise as well as preserve the edges. The main drawback of a standard median filter (SMF) [7], [8] is that it is effective only for low noise densities. At high noise densities, SMFs often exhibit blurring for large window sizes and insufficient noise suppression for small window sizes. However, most of the median filters operate uniformly across the image and thus tend to modify both noise and noise-free pixels. Consequently, the effective removal of impulse often leads to images with blurred and distorted features. Ideally, the filtering should be applied only to corrupted pixels while leaving uncorrupted pixels intact [9]. Applying median filter unconditionally across the entire image as practiced in the conventional schemes would inevitably alter the intensities and remove the signal details of uncorrupted pixels. Therefore, a noise-detection process to discriminate between uncorrupted pixels and the corrupted pixels prior to applying nonlinear filtering is highly desirable [10]. Weighted median filter have caught ample attention in signal and image processing applications [11]. Considered as a generalization of the classical median filter, weighted median filters (WMF) have excellent detail preserving and noise suppression characteristics. Noise reduction, image restoration and field interpolation are only a few of the areas where WMF s have been applied. Despite their popularity, digital implementations of WMF are computationally expensive [11], [12] because they need to perform, when required, a sorting operation and a strategy for duplication for each pixel. Despite some works have been directed to

2 34 International Journal of Computational Intelligence & Telecommunication Systems reduce the number of data involved in the weighted median computations [13], massive applications of median filters by using digital techniques remains unsolved. Thus a technique with lower computations and altering only the corrupted pixels is proposed in this paper. Earlier algorithms use combinations of row, column and diagonal sorting [14] which increases computational and hardware complexity. Also decrease in operating speed due to more computations is observed. But the Lone Diagonal Sorting (LDS) algorithm proposed in this paper uses diagonal sorting alone to obtain appreciable results in terms of computational complexity and visual appearance than existing algorithms. II. LONE DIAGONAL SORTING ALGORITHM The algorithm is explained with the following steps: STEP 1: A sliding window of 3 x 3 in a 512x512 image is taken. STEP 2: The leading diagonal elements of the 3 x 3 matrix is taken and sorted. STEP 3: The values are checked for salt and pepper noise (0 or 255) and replaced with either of the other two values which is non-noisy. STEP 4: Shift pulse is applied to move to the next 3 x 3 sliding window. STEP 5: The same process stated in STEP 3 is repeated for the entire image. Sorting is the important step involved in denoising of an image. There are various sorting algorithms such as binary sort, bubble sort, merge sort, quick sort, shear sort, etc. The proposed algorithm employs the sorting of the diagonal elements alone and hence reducing the computational complexity. After denoising the first 3X3 window, the window is shifted in the horizontal direction once to obtain the next 3X3 window and the procedure is repeated as stated above. The corner pixels can be accordingly padded in order to obtain 3x3 window. Thus 512x512 pixels can be processed by applying horizontal and vertical shifts suitably and hence successful denoising of the image is achieved within a short span of time. The illustration of lone diagonal sorting is shown in Figure 1-5. Figure 1: Figure 2: Figure 3: Figure 4: Figure 5: Selection of 3X3 Matrix Original Matrix before Sorting Step 1-diagonal Sorting Step 2-replacement of Noisy Pixel Step 3-denoised 3X3 Window

3 A Robust Lone Diagonal Sorting Algorithm for Denoising of Images with Salt and Pepper Noise 35 The illustration of LDS algorithm is shown in the table I containing the comparison of the various sorting techniques. It is observed that only 3 comparisons are required to compute a median 3X3 window, thus resulting in a drastic improvement of computational complexity and hence the computational time required for denoising the image. Table I Comparison of the Various Sorting Techniques (a) (b) Sorting techniques No of comparisons required to compute median 3X3 window Bubble sort 36 Shear sort 18 Lone diagonal sort 3 III. RESULTS AND DISCUSSION The developed algorithm is tested using 512X512 image, Lena (gray), cameraman(gray), boat(gray). The performance of the proposed algorithm is tested for all levels of noise corruption (upto 90%). Each time the test image is corrupted by salt and pepper noise of different density ranging from 10% to 90% with an increment of 10% and tested for denoising. The results obtained are hence shown in figure 6-8. Figure 7: (c) Results obtained for noise corrupted 512X512 cameraman image. (a), (b) are the noise corrupted cameraman image with noise densities 10% and 60% respectively and (c), (d) are the corresponding restored images (d) (1) (b) (a) (b) Figure 6: (c) Results obtained for noise corrupted 512X512 lena image. (a) (b) are the noise corrupted lena image with noise densities 10% and 60% respectively and (c), (d) are the corresponding restored images (d) Figure 8: (c) Results obtained for noise corrupted 512X512 image. (a), (b) are the noise corrupted lena and cameraman image of noise density 90% and (c), (d) are the corresponding restored images The performance of the proposed algorithm is tested for various levels of noise corruption and (d)

4 36 International Journal of Computational Intelligence & Telecommunication Systems compared with standard filters namely Standard Median Filter (SMF) and Weighted Median Filter (WMF). The performance of the developed algorithm and other standard algorithms are quantitatively measured by the following parameters such as peak signal-to-noise ratio (PSNR) and Mean square error (MSE). They are defined by the following formulae (1) and (2). [6] Where, PSNR=10 log 10 (255 2 /MSE) (1) m n MSE = x= 1 y= 1(( f,)( x y,)) f x y (2) Where M and N are the total number of pixels in the horizontal and the vertical dimensions of the image, f and f denote the original and filtered image respectively. The PSNR and MSE values are compared with the other algorithms and shown in Tables [II],[III] and the comparison plots are shown in Figure Table II Comparison Table of PSNR of Different Filters for lena.png (512 x 512) Image Noise Densities(%) SMF WMF Proposed LDS Algorithm Thus the above plot clearly shows that the proposed Lone Diagonal Sorting algorithm has higher values of PSNR for all noise densities than the standard methods Standard Median Filter and Weighted Median Filter. The proposed algorithm has high noise rejection even at higher noise densities as depicted in the above graph. Table III Comparison Table of MSE of Different Filters for lena.png (512 x 512) Image Noise Densities(%) SMF WMF Proposed LDS Algorithm Figure 10: Comparison Graph of MSE Values at Different Noise Densities for Lena Image Figure 9: Comparison Graph of PSNR Values at Different Noise Densities for Lena Image The graph which depicted above shows the comparison of Mean Square Error of proposed LDS algorithm with other algorithms. It is clearly shown that MSE values are drastically reduced for all noise densities when compared with SMF and WMF. Even for noise densities above 60%, the proposed algorithm gives very less MSE. Thus the quantitative measures show that the LDS algorithm gives appreciable results comparatively. The Structural Similarity (SSIM) index is a method for measuring the similarity between two

5 A Robust Lone Diagonal Sorting Algorithm for Denoising of Images with Salt and Pepper Noise 37 images. The SSIM index can be viewed as a quality measure of one of the images being compared provided the other image is regarded as of perfect quality. It is an improved version of the universal image quality index proposed before. SSIM( x,) y (2)(2) µ xµ y + c1 σ xy + c2 = ()() µ + µ + c σ + σ + c (3) x y 1 x y 2 µ x is the average of x, µ y is the average of y, σ x2 is the variance of x, σ y2 is the variance of y, σ xy is the covariance of x and y. c 1 = (k 1 L) 2, c 2 = (k 2 L) 2 are the two variables to stabilize the division with weak denominator. Where k 1 =0.01 and k 2 =0.03 by default. #bits per L is the dynamic range of the pixel-vales (2 pixel -1). Table IV Table Showing the SSIM for lena.png (512x512) Image Noise Density (%) SSIM The computational time required for denoising the lena.png (512X512) image with various noise densities is shown in Table IV. The algorithm was implemented in MATLAB 7.1 on a PC equipped with 2.4GHz CPU and 1 GB RAM memory for the evaluation of computational time. Table V Computational Time for Denoising lena.png (512 x 512) Image % of noise Computational time (s) The above results from the table depicts that the computational time remains constant (approx.) irrespective of the noise density for the proposed algorithm. This proves the stability of the LDS algorithm. IV. CONCLUSION & FUTURE WORK An efficient non-linear algorithm to remove salt and pepper noise is proposed. The Lone Diagonal Sorting algorithm clearly reduces the computational time required for denoising the corrupted images. Also since the noisy pixels are replaced with the immediate neighborhood pixels, the image quality is comparatively appreciable. The lower number of computations performed obviously reduces the hardware complexity, thereby increasing the efficiency and reducing the cost of the system compared to the other competitive algorithms. This algorithm can be expanded and applied over noise affected RGB images and Video signals. REFERENCES [1] I. Pitas and A.N. Venetsanopoulous, Non-linear Digital Filter Principles and Applications, (Boston: Kluwer Academic publishers, 1990). [2] J. Astola and P. Kuosmanen, Fundamentals of Non- Linear Digital Filtering, BocRaton, CRC, [3] Rafeal C. Gonzales and Richard E. Woods Digital image Processing Pearson Education, [4] Sung-Jea Ko, and Yong Hoon Lee, Center weighted median filters and their applications to image enhancement, IEEE Trans. Circuits and Systems, Vol. 38, No. 9, pp , [5] Wenbin Luo, Efficient removal of impulse noise from digital images, IEEE Trans. [6] A. C. Bovik., Streaking in median filtered images, IEEE Trans. Acoust., Speech,Signal Processingn., Vol. 35, pp , [7] N. C. Gallagher, Jr. and G.L.Wise, A Theoretical Analysis of the Properties of Median Filters, IEEE Trans. Acoust., Speech and Signal Processing, Vol. ASSP-29, pp , [8] T. A. Nodes and N. C. Gallagher, Median Filters: Some Modifications and their properties, IEEE Trans. Acoust., Speech and Signal Processing, Vol. ASSP-30, pp , [9] W. Luo, An efficient detail-preserving approach for removing impulse noise in images, IEEE Signal Process. Lett., Vol. 13, No.7, 2006, pp [10] R. H. Chan, C.W. Ho, and M. Nikolova, Salt and pepper noise removal by median type noise detectors and detail preserving regularization,

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