Centralized sparse representation for image restoration

This paper proposes a novel sparse representation model called centralized sparse representation (CSR) for image restoration tasks. In order for faithful image reconstruction, it is expected that the sparse coding coefficients of the degraded image should be as close as possible to those of the unknown original image with the given dictionary. However, since the available data are the degraded (noisy, blurred and/or down-sampled) versions of the original image, the sparse coding coefficients are often not accurate enough if only the local sparsity of the image is considered, as in many existing sparse representation models. To make the sparse coding more accurate, a centralized sparsity constraint is introduced by exploiting the nonlocal image statistics. The local sparsity and the nonlocal sparsity constraints are unified into a variational framework for optimization. Extensive experiments on image restoration validated that our CSR model achieves convincing improvement over previous state-of-the-art methods.