Image Restoration via Group l2,1 Norm-Based Structural Sparse Representation

Abstract

Sparse representation has recently been extensively studied in the field of image restoration. Many sparsity-based approaches enforce sparse coding on patches with certain constraints. However, extracting structural information is a challenging task in the field image restoration. Motivated by the fact that structured sparse representation (SSR) method can capture the inner characteristics of image structures, which helps in finding sparse representations of nonlinear features or patterns, we propose the SSR approach for image restoration. Specifically, a generalized model is developed using structured restraint, namely, the group [Formula: see text]-norm of the coefficient matrix is introduced in the traditional sparse representation with respect to minimizing the differences within classes and maximizing the differences between classes for sparse representation, and its applications with image restoration are also explored. The sparse coefficients of SSR are obtained through iterative optimization approach. Experimental results have shown that the proposed SSR technique can significantly deliver the reconstructed images with high quality, which manifest the effectiveness of our approach in both peak signal-to-noise ratio performance and visual perception.