Nonconvex Lp Nuclear Norm based ADMM Framework for Compressed Sensing
Compressed Sensing (CS) has drawn quite an amount of attention as a joint sampling and compression methodology. Recent studies further show that image prior models play an important role in image CS recovery. By exploiting the non-local self-similarity of natural images and clustering similar patches, low-rank prior model is adopted in this paper. Different from traditional nuclear norm, we extend the lp (0 <; p <; 1) penalty function on singular values of a matrix to characterize low-rank prior model, and propose a new non-nonvex lp nuclear norm prior model for image CS recovery, which is able to more accurately enforce image structural sparsity and self-similarity at the same time. The proposed optimization problem is efficiently solved within the alternative direction multiplier method (ADMM) framework. Experimental results demonstrate that the proposed lp nuclear norm based ADMM framework for image CS recovery framework exhibits good convergence and achieves significant performance improvements over the current state-of-the-art methods.