Adaptive group sparse representation for image compressive sensing

Abstract

Group sparse representation has raised lots of powerful signal recovery techniques in various compressive sensing studies, which can be considered as a low rank matrix approximation problem. Recent advances have suggested the adaptive singular value thresholding for low rank recovery under affine constraints. In this paper, we propose an adaptive group sparse representation for image compressive sensing recovery. A framework based on alternating direction method of multipliers is presented, where the adaptive singular value thresholding is introduced to solve the group sparse representation problem. In this method, the threshold adaptively decreases during iterations, instead of the traditional methods where the threshold level is independent of the iteration number. The simulation results reveal that the proposed method achieves a good convergence performance and improves the compressive sensing recovery quality significantly compared with the state-of-the-art methods.