Comparative study of non-convex penalties and related algorithms in compressed sensing

Abstract

Non-convex penalties are widely used in sparse representation models and fields such as compressed sensing, because they can efficiently recover signals with a high sparsity level compared with the well-known ℓ1-norm. However, few classic penalties have been selected in most applications without exploring the performance of other non-convex penalties. Therefore, the objective of this study is to provide a comparative and comprehensive study on non-convex penalties. We first collected nine representative non-convex penalties and then applied two optimization frameworks: the difference of convex function algorithm (DCA) and iterative shrinkage/thresholding algorithm (ISTA) to solve the optimization problems associated with the nine non-convex penalties. The performances of the nine penalties and two algorithms were systematically compared and analyzed experimentally. We hope that these results that concern non-convex penalty selection in sparse representation models can be used as a general reference for research.