Multiple-prespecified-dictionary sparse representation for compressive sensing image reconstruction with nonconvex regularization

Abstract

Multiple-prespecified-dictionary sparse representation (MSR) has shown powerful potential in compressive sensing (CS) image reconstruction, which can exploit more sparse structure and prior knowledge of images for minimization. Due to the popular L1 regularization can only achieve the suboptimal solution of L0 regularization, using the nonconvex regularization can often obtain better results in CS reconstruction. This paper proposes a nonconvex adaptive weighted Lp regularization CS framework via MSR strategy. We first proposed a nonconvex MSR based Lp regularization model, then we propose two algorithms for minimizing the resulting nonconvex Lp optimization problem. According to the fact that the sparsity levels of each regularizers are varying with these prespecified-dictionaries, an adaptive scheme is proposed to weight each regularizer for optimization by exploiting the difference of sparsity levels as prior knowledge. Simulated results show that the proposed nonconvex framework can make a significant improvement in CS reconstruction than convex L1 regularization, and the proposed MSR strategy can also outperforms the traditional nonconvex Lp regularization methodology.