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Image Denoising Based On Sparse Representation In A Probabilistic Framework
Mohamed EL-Sayed Waheed, Hassan Ahmad Khalil, Osama Farouk Hassan
Pages - 20 - 29     |    Revised - 01-06-2014     |    Published - 01-07-2014
Volume - 8   Issue - 3    |    Publication Date - July 2014  Table of Contents
Sparse Representation, Image Denosing, Independent Component Analysis, Dictionary Learning.
Image denoising is an interesting inverse problem. By denoising we mean finding a clean image, given a noisy one. In this paper, we propose a novel image denoising technique based on the generalized k density model as an extension to the probabilistic framework for solving image denoising problem. The approach is based on using overcomplete basis dictionary for sparsely representing the image under interest. To learn the overcomplete basis, we used the generalized k density model based ICA. The learned dictionary used after that for denoising speech signals and other images. Experimental results confirm the effectiveness of the proposed method for image denoising. The comparison with other denoising methods is also made and it is shown that the proposed method produces the best denoising effect.
CITED BY (1)  
1 Xuan, S., & Han, Y. (2015). Improved extreme value weighted sparse representational image denoising with random perturbation. Journal of Electronic Imaging, 24(6), 063004-063004.
1 Google Scholar 
2 CiteSeerX 
3 refSeek 
4 Scribd 
5 SlideShare 
6 PdfSR 
A. Hyvärinen, "Sparse coding shrinkage: denoising of nongaussian data by maximum likelihood estimation", Neural Computation, 11 , pp. 1739–1768, 1997.
A. Hyvärinen, E. Oja, "A fast fixed-point algorithm for independent component analysis",Neural Comput. , 9, pp. 1483-1492, 1997.
A. Hyvärinen, R. Cristescu, E. Oja, "A fast algorithm for estimating overcomplete ICA bases for image windows", in:Proc. Int. Joint Conf. on Neural Networks, Washington, D.C., pp. 894-899, 1999.
A. J. Bell and T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution”, Neural Comp., 7, pp. 1129-1159, 1995.
Aharon M., Elad M., Bruckstein A. "K-SVD: An Algorithm for Designing OvercompleteDictionaries for Sparse Representation", IEEE Trans. on Signal Processing,54(11),November 2006.
BaraniukR.G., V. Cevher, M.F. Duarte, and C. Hegde, "Model-based compressive sensing",Preprint, 2008.
Clementi F, Gallegati M, Kaniadakis G, "A new model of income distribution: The kgeneralized distribution", Empir Econ , 39: pp. 559–591, 2011.
Coifman, R., Donoho, D.L., "Translation invariant de-noising", In: Wavelets andStatistics.Lecture Notes in Statistics, pp. 125–150. Springer, New York ,1995.
D. Erdogmus, K. E. Hild II, Y. N. Rao and J.C. Principe, “Minimax Mutual Information Approach for Independent Component Analysis”, Neural Computation, vol. 16, No. 6, pp.1235-1252
D.M. Chandler, D.J. Field., "Estimates of the Information content and dimensionality of natural scenes from proximity distributions", Journal of the Optical Society of America A,24(4) , pp. 922–941, 2007.
DaubechiesI., M. Defrise, and C. De Mol., "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint", Comm. Pure Appl. Math., 57: pp. 1413–1457,2004.
Diversi R.,Guidorzi R. ,Soverini U. , "Blind identification and equalization of two-channel FIR systems in unbalanced noise environments", Signal Processing , vol. 85, pp. 215–225, 2005.
Donoho D.L. " De-noising by soft thresholding", IEEE Trans. Inf. Theory , 41(3), pp. 613–627, 1995.
E.J. Candes and D.L. Donoho,"New tight frames of curvelets and optimal representations of objects with C2 singularities", Comm. Pure Appl. Math., 56: pp.219–266, 2004.
EfronB., T. Hastie, I. Johnstone, and R. Tibshirani, "Least angle regression". Annals of Statistics, 32(2): pp. 407–451, 2004.
EladM. and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries", IEEE Trans. On Image Proc., 15(12): pp.3736–3745, 2006.
Gilboa, G., Sochen, N., Zeevi, Y., "Forward-and-Backward Diffusion Processes for Adaptive Image Enhancement and Denoising", IEEE Trans. on Image Processing ,11(7), pp. 689–703, 2002.
Grace Chang S., Yu B., Vetterli M., "Adaptive wavelet thresholding for image denoising and compression", IEEE Trans. on Image Processing, 9(9), pp. 1532–1546 , 2000.
Huang J., T. Zhang, and D. Metaxas, "Learning with structured sparsity", In Proceedings of the 26th Annual International Conference on Machine Learning, pp. 417–424. ACM, 2009.
Lagarias J. C. ,Reeds J.A.,Wright M.H., Wright P.E., "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. ,9(1) ,pp. 112-147,December 1998.
MairalJ., M. Elad, and G. Sapiro, "Sparse representation for color image restoration", IEEE Trans. on Image Proc., pp. 17, 2008.
MallatS. and G. Peyr´e, "Orthogonal band let bases for geometric images approximation",Comm. Pure Appl. Math., 61(9): pp. 1173– 1212, 2008.
MallatS. and G. Yu., "Super-resolution with sparse mixing estimators", Accepted to IEEE Trans. on Image Proc., 2010.
MallatS., "A Wavelet Tour of Signal Proc.: The Sparse Way", 3rd edition, Academic Press,2008.
Mihcak, M.K., Kozintsev, I., Ramchandran, K., Moulin, P., "Low complexity image denoising based on statistical modeling of wavelet coefficients", IEEE Signal Processing Letters ,6(12),pp. 300–303 ,1999.
Neelamani R., H. Choi, and R. Baraniuk, "Forward: Fourier-wavelet regularized deconvolution for ill-conditioned systems", IEEE Trans. on Signal Proc., 52(2): pp. 418–433,2004.
P. Hoyer, A. Hyvärinen, E. Oja, "Sparse coding shrinkage for image denoising", in neural networks proceedings, IEEE World Congress on Computation an intelligence ,2, pp.859–864, 1998.
Shin J. W. Chang J. H., Kim N. S., "Statistical modeling of speech signals based on generalized gamma distribution", IEEE Signal Process. Lett., 12 (3) , pp. 258-261, March 2005.
Starck J., Candes E., Donoho D.L., "The curvelet transform for image denoising", IEEE Trans on Image Processing, 11(6), pp. 670–684 , 2002.
Weisheng D., Xi L., Lei Z., Guangming S., "Sparsity-based Image Denoising via Dictionary Learning and Structural Clustering" , Computer Vision and Pattern Recognition (CVPR),IEEE Conference, pp. 457 – 464, 2011.
Dr. Mohamed EL-Sayed Waheed
Faculty of Computers & Informatics / Department of Computer Science Suez Canal University Ismailia, Egypt - Egypt
Dr. Hassan Ahmad Khalil
Faculty of Science / Department of Mathematics Zagazig University Zagazig, Egypt - Egypt
Dr. Osama Farouk Hassan
Qassim university - Egypt