Image denoising via overlapping group sparsity using orthogonal moments as similarity measure.

Recently, sparse representation has attracted a great deal of interest in many of the image processing applications. However, the idea of self-similarity, which is inherently present in an image, has not been considered in standard sparse representation. Moreover, if the dictionary atoms are not constrained to be correlated, the redundancy present in the dictionary may not improve the performance of sparse coding. This paper addresses these issues by using orthogonal moments to extract the correlations among the atoms and group them together by extracting the characteristics of the noisy image patches. Most of the existing sparsity-based image denoising methods utilize an over-complete dictionary, for example, the K-SVD method that requires solving a minimization problem which is computationally challenging. In order to improve the computational efficiency and the correlation between the sparse coefficients, this paper employs the concept of overlapping group sparsity formulated for both convex and non-convex denoising frameworks. The optimization method used for solving the denoising framework is the well known majorization-minimization method, which has been applied successfully in sparse approximation and statistical estimations. Experimental results demonstrate that the proposed method offers, in general, a performance that is better than that of the existing state-of-the-art methods irrespective of the noise level and the image type.