MAP-based image denoising with structured sparsity and Gaussian scale mixture

Image denoising is a classical problem in image processing and is known to be closely related to sparse coding. In this work, based on the key observation that the probability density function (PDF) of image patch is relevant to the maximum a posteriori estimation of sparse coefficients, using an efficient approximation of the PDF of image patch, a nonlocal image denoising method: improved simultaneous sparse coding with Gaussian scale mixture (ISSC-GSM) is proposed. The preprocessing of centering for a collection of similar patches saves expensive computation and admits biased-mean of sparse coefficients. Our formulation can be efficiently computed by alternating minimization, and both subproblems have analytical solutions using the orthogonal PCA dictionary. When applied to noise removal, the proposed ISSC-GSM has achieved highly competitive denoising performance with often higher subjective and objective qualities than other competing approaches. Experimental results have shown that our method often provides the best visual quality by effectively suppressing undesirable artifacts while maintaining the textures and edges, which is most suitable for processing images with abundant self-repeating patterns.