COMPARISON BETWEEN K_SVD AND OTHER FILTERING TECHNIQUE

COMPARISON BETWEEN K_SVD AND OTHER FILTERING TECHNIQUE Anuj Kumar Patro Manini Monalisa Pradhan Gyana Ranjan Mati Swasti Dash Abstract The field of image de-noising sometimes referred to as image deblurring or image (de-convolution) is concerned with the reconstruction or estimation of the encrypted image from a blurred and noisy one.. SVD process is then employed for the noisy images in order to remove noise from the input images. The noisy image is divided into patches. The SVD denoising process is applied to the identified patches in the images. The objective of the paper is to perform analysis of different types of non linear filters and calculate their PSNR, FSIM value according noise density. keyword:k- SVD, PSNR, FSIM I.INTRODUCTION Noise elimination is a main concern in computer vision and image processing. A digital filter [1] is used to remove noise from the degraded image. As any noise in the image can be result in serious errors. Noise is an unwanted signal, which is manifested by undesirable information. Thus the image, which gets contaminated by the noise, is the degraded image and using different filters can filter this noise. Thus filter is an important subsystem of any signal processing system. Thus filters are used for image enhancement, as it removes undesirable signal components from the signal of interest [2]. The process of image denoising process is implemented based on the SVD algorithm for the efficient removal of noises in the images[3]. Initially noise is added to the images based on the random noise generated. The dictionary is created for the images in order to identify the noise locations in the images. The clustering process groups the noise locationsin the images based on the difference in the noise locations in the images. Optimization of images is based on the Low Rank optimization process. Finally, structured sparse representation is employed for the images to reconstruct the high-resolution images. The performance of the process is measured with the help of performance metric like PSNR, FSIM. II.METHODS There are basically two noises considered such as Gaussian noise and impulse noise. Several noise density like low (0.4) has been implemented.[4]. Likewise the Gaussian noise with variance 0.01 and has been evaluated using standardize (boy.bmp) image of size 256*256 and of bit 8 bit is take-in in to the consideration. Filter add used for de-noising the image corrupted with impulse noise [5]The performance can be analyzed through the basic PSNR and FSIM matrices[6].the quality of denoised image can be calculated by the highest peak 335

signal noise ratio PSNR=10 log 10 2 as proposed algorithm has ability to reduce the high density of the noise. The process of image denoising process is implemented based on the SVD algorithm for the efficient removal of noises in the images[6]. = Patch grouping process is employed based on Initially noise is added to the images based on the measurement of similarity identification based random noise generated. The dictionary is created for clustering of the patches based on Fuzzy C means. the images in order to identify the noise locations in Fuzzy C means process identifies the pixels that were the images. The clustering process groups the noise similar and groups them into a single cluster. locations in the images based on the difference in the In the back propagation process, the noises in the noise locations in the images. Optimization of images images occurring due to the pixel grouping based on is based on the Low Rank optimization process. the low rank approximation are Finally, structured sparse representation is employed removed.[10].performance of the enhancement for the images to reconstruct the high-resolution process is measured based on the PSNR and FSIM images. The performance of the process is measured calculation [11]. with the help of performance metric like PSNR, FSIM The calculated performance metrics indicates that the [7]. proposed method is more efficient compared to the Input SVD patch image Denoising grouping Back propagation Performance Measures Optimization calculated dictionary based on SVD process is then optimized resulting in the patch grouping process. The optimization process is employed based on Low rank approximation process. The low rank approximation process minimizes the overall errors in the obtained de-noised image. [9] = 2 + ( ) + ( ) existing methods. III.ALGORITHIM Algorithms1: The K-means algorithms Step-1; Task for a: Select best possible code for represent data { } 1 as and adjacent. b: solving by:, { } 2 subject to for same k Step2: Initialization. a: Set the code matrix c (o) R n K Fig1.Block diagram of K-SVD denoisng process SVD Process is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to fit the data better.[8] Low-Rank b: Set J=1 c: Step3: Repeat until close (use stop rule) i) Sparse coding: a: Divide the training samples y in k sets by { 1( 1), 2( 1). ( 1) } b: each process the sample same to the column ( 1) 336

( 1) = { ( 1) 2 ii) Codes update: a: each column k in c (J-1) update using ( ) 1 = ( 1) ( 1) 2 } = U V T Select update column dk to the first column U Update coefficient vector multiplied by (1,1) iii) set J= J+1 IV.RESULTS AND ANALYSIS iii) set J= J+1 Algorithms2: The K-SVD algorithms Step-1; Task for a: Select best source data for { } 1 as sparse organise. b: solving by:, { } 2 subject to 0 T0 Step2: Initialization. a: Set the source c (o) R n K with l 2 normalized columns b: Set J=1 Step3: Repeat until close (use stop rule) i) Sparse coding: a: use any detection algorithm to compute represent vector xi for example yi i=1,2, 2 N { } Output Images from Different De-noising Process at Impulse noise density (0.4) 2 subject to 0 T0 ii) Codes update: Each column k =1,2,3,..K D (J-1) update by a: Define the examples use k={ i 1 i N (i) 0} b: compute the total representation error matrix Ek E k= c: Resticted Ek columns corresponding k obtain d: Apply SVD decomposition Fig2(j)K-SVD denoising (PSNR-24.0543dB) 337

Denoising Process Center weight Median Filter PSNR value FSIM in db 16.7836 0.4765 The plot Figure shows the PSNR AND FSIM values Of different de-noising algorithms and filters. The K- SVD de-noising algorithm gives better result than other de-noising filters and algorithms Median Filter 18.278 0.5541 2nd Order Median Filter 20.4597 0.7096 3rd Order Median Filter 20.5797 0.718 Decision Based Algorithm For Removal 24.4304 0.8078 Of Impulse Noise Fig2(c).FSIM Value of Different De-noising Process After considered the impulse noise at noise density(0.4) here the Gaussian Noise is to be taken in to Consideration. Here boy standardize image of size 256*256 of bit of is also taken and PSNR and FSIM values are calculated at variance of 0.01, for the different de-noising process. The performance graphs are plotted. Adaptive Median Filter 27.345 0.8094 Noise Adaptive Fuzzy Switching Median 30.0523 0.8147 Filter Denoisin K-SVD g Algorithm 24.0543 0.8256 Table: 2(a)PSNR FSIM Value of different Denoising algorithms and filters 338

PSNR in db M Value Proceedings of International Interdisciplinary Conference On Engineering Science & Management Held 1 0.5 0 Fig3(j)KSVDdenoising(19.9724dB) Denoising process PSNR in FSIM db value Median Filter 27.2175 0.6253 2nd Order Median Filter 22.1898 0.5347 3rd Order Median Filter 22.1797 0.5324 Switching Median Filter 22.4545 0.5743 Fig 3(c). Different FSIM values at Variance (0.01) Comparison of PSNR and FSIM value ofadaptive Median Filter and K-SVD de- noising process are presented for Gaussian Noise at different variance (0.02, 0.0.05, 0.09) among the nonlinear filters the adaptive median filter gives the better result than other nonlinear filters. Here a comparison has been made among the adaptive median filter and K-SVD denoising algorithm [8]. Center weight Median Filter 23.9996 0.6026 Adaptive Median Filter 24.6742 0.6928 K-SVD Denoising algorithim 24.9047 0.8469 Comparison of PSNR and FSIM value Gaussian noise(.01) Vaiance (0.05) 50 40 30 20 10 0 FIG:3(b) PSNR values at variance (0.01) Variance (0.09) 339

FFig-4 Comparison between Adaptive Median Filter and KSVD Denoising PSNR value at 0.02, 0.05,0.09 Table 4(a): FSIM Values of Adaptive Median Filter and K-SVD De-noising Process Fig- 4(b)FSIM Value of Adaptive Median Filter and K-SVD denoising Process V. CONCLUSION In this paper, we focused on the image denoising through non-linear filters which have reduced the complexity some to extend. The non-linear filter does not applicable for all the noises and not permeable to restore the original properties. In this paper Image denoising through K-SVD algorithm is presented as well as comparison with other filters are done by taking the standardize image. The performance matrices PSNR and FSIM have been calculated. The K-SVD algorithm reduces the complexity. REFERENCES [1] C. Kervrann and J. Boulanger, Local adaptivity to variable smoothness for exemplar-based image regularization and representation, Int. J. Comput. Vision, vol. 79, no. 1, pp. 45 69, Nov. 2007 [2] L. Shao, R. Yan, X. Li, and Y. Liu, From heuristic optimization to dictionary learning: a review and comprehensive comparison of image denoising algorithms, IEEE Trans. Cybern., vol. 44, no. 7, pp. 1001 1013, Jul. 2014. [3] K. Kreutz-Delgado, J. F. Murray, B. D. Rao, K. Engan, T. Lee, and T. J. Sejnowski, Dictionary learning algorithms for sparse representation, Neural Comp., vol. 15, no. 2, pp. 349 396, 2003 [2] A Novel Method of Image Restoration by using Different Types of Filtering Techniques,Anamika Maurya, Rajinder, TiwariInternational Journal of Engineering Science and Innovative Technology (IJESIT) Volume 3, Issue 4, July 2014. [3] Charu Khare, Kapil Kumar Nagwanshi Image Restoration Technique with Non LinearFilters Computer Science Department, Chhattisgarh Swami Vivekananda Technical University Rungta College of Engineering & Technology, Bhilai, INDIA International Journal of Engineering Trends and Technology- May to June Issue 2011. [4] K. Engan, B. D. Rao, and K. Kreutz-Delgado, Frame design using focuss with method of optimal directions (mod), in Norwegian Signal Process. Symp., 1999, vol. 65-69. 340

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