Digital Image Sparse Denoising Based On Dictionary Learning And Greedy Pursuit Algorithm

Fix transform basis and cascade multiple transform basis are used for dictionary construction in traditional denoising model based on sparse representation. However, definite fix transform basis can’t represent various structures of natural images effectively. Learning dictionary improves the representation ability of traditional dictionary which matches image internal structure better. Overcomplete dictionary also ensures the efficiency and robustness of the sparse decomposition based on dictionary. Choosing a group of the most sparse combinations of atoms from overcomplete space to approximate original image is a NP-hard problem, greedy tracking algorithm is usually used to solve the problem because of lower complexity. However the adaptive sparsity estimation and backtracking optimization atomic choice cannot achieve balance and unity well. Therefore, the main contributions of this paper are:1. In order to address the problems of poor efficiency of sparsity adaptive estimation and backtracking optimization when using sparse decomposition in fixed dictionary to denoising images, a method of K-Singular Value Decomposition is used to learn the over-complete dictionary based on the characteristics of the internal structure of the noisy images. Consequently, the method enhances the representation ability of the dictionary. Furthermore, the Adaptive Sparsity Matching Pursuit algorithm is used for estimating the image sparsity adaptively, and the backtracking optimization is applied when choosing atoms to reduce artificial blindness while setting image sparsity and to enhance the robustness of the algorithm at the same time. Experimental results show that digital image sparse denoising based on K-SVD and ASMP algorithm gains better Peak Signal to Noise Ratio (PSNR) when compared with the traditional sparse denoising approach.2. In order to reduce the influence of noise in ASMP algorithm to sparseness estimation and avoid time consume caused by iteration, Backtracking-based Adaptive Orthogonal Matching Pursuit (BAOMP) method is used on the basis of K-SVD learning dictionary. Atoms are selected and deleted according to amplitude of atom which have the maximum similarity. BAOMP is more simple and flexible during the procedure of atom selection and atom set optimization. Experimental results show that BAOMP sparse decomposition denoising algorithm in the K-SVD learning dictionary has better denoising performance and less running time than the algorithm of K-SVD and ASMP.In summary, our algorithms have outstanding performance in digital image denoising, not only improved the traditional dictionary representation performance, but also optimized atomic structure in the dictionary. Sparse decomposition based on dictionary can quickly match the best group of atoms to approximately fitting original image. Furthermore, in the circumstances of unknown image sparseness, successive approximation and atom back-tracking method are used to estimate image sparseness in accordance with signal measure distribution, improve the robustness of this algorithm and increase the accuracy of sparse decomposition de-noising algorithm based on learning dictionary.