Nonconvex Is Attractive: L2/3 Regularized Thresholding Algorithm Using Multiple Sub-Dictionaries

The L
_2/3
-regularization is a typical nonconvex and nonsmooth optimization method, which can obtain more powerful performance than L
₁
regularization in some applications, such as computational imaging, sparse signal recovery and low-rank matrix completion, etc. This paper proposes an adaptive iteratively-weighted thresholding algorithm for L
_2/3
-regularized problem based on the multiple analysis sub- dictionaries (MD) sparsifying transform strategy, the MD strategy can be employed to further exploit the prior knowledge of estimated signal for sparse recovery. What's more, we propose an adaptive updating scheme for regularization parameter to weight the contribution of each sub-dictionary. Experiments confirm that the proposed method could obtain higher image quality and achieve faster convergence than some corresponding prior work.