Group-Based Sparse Representation for Image Restoration

TLDR

Traditional patch‑based sparse representation of natural images suffers from high computational cost in dictionary learning and ignores inter‑patch relationships, leading to inaccurate sparse coding. The authors introduce group‑based sparse representation (GSR), using groups of nonlocal patches as the basic unit to model natural images. GSR jointly enforces local sparsity and nonlocal self‑similarity, employs a low‑complexity self‑adaptive dictionary per group, and solves the resulting ℓ0 minimization with a split Bregman technique. Experiments on inpainting, deblurring, and compressive sensing demonstrate that GSR outperforms state‑of‑the‑art methods in PSNR and visual perception.

Abstract

Traditional patch-based sparse representation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational complexity in dictionary learning. Second, each patch is considered independently in dictionary learning and sparse coding, which ignores the relationship among patches, resulting in inaccurate sparse coding coefficients. In this paper, instead of using patch as the basic unit of sparse representation, we exploit the concept of group as the basic unit of sparse representation, which is composed of nonlocal patches with similar structures, and establish a novel sparse representation modeling of natural images, called group-based sparse representation (GSR). The proposed GSR is able to sparsely represent natural images in the domain of group, which enforces the intrinsic local sparsity and nonlocal self-similarity of images simultaneously in a unified framework. In addition, an effective self-adaptive dictionary learning method for each group with low complexity is designed, rather than dictionary learning from natural images. To make GSR tractable and robust, a split Bregman-based technique is developed to solve the proposed GSR-driven ℓ0 minimization problem for image restoration efficiently. Extensive experiments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed GSR modeling outperforms many current state-of-the-art schemes in both peak signal-to-noise ratio and visual perception.