Image compressed sensing recovery via nonconvex garrote regularization

Abstract

Sparsity inducing model is one of the most important components of image compressed sensing (CS) recovery methods. These models are built on the image prior knowledge. The model which can reflect the image priors appropriately, yields high quality recovery results. Recent studies have shown that nonlocal low-rank prior based models often lead to superior results in CS recovery. The rank regularization problem resulting from these models is an NP-hard problem and how to solve it has a great impact on the recovery results. In this paper, we propose a new CS recovery method via nonconvex Garrote regularization (NGR) toward better exploiting the nonlocal low-rank prior. In the proposed CS-NGR method, the nonconvex Garrote function is introduced as a suitable surrogate for the rank function. To solve the resulting minimization problem efficiently, we employ the alternating direction method and so-called Garrote singular value shrinkage (GSVS) technique. Extensive experimental results show effectiveness of the proposed method compared with the state-of-the-arts methods in CS image recovery.