ADMM-IDNN: Iteratively Double-reweighted Nuclear Norm Algorithm for Group-prior based Nonconvex Compressed Sensing via ADMM

Group-prior based regularization method has led to great successes in various image processing tasks, which can usually be considered as a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex surrogate usually lead to over-shrinking phenomena, since the nuclear norm shrinks the rank components (singular value) simultaneously. In this paper, we propose a novel Group-prior based nonconvex image compressive sensing (CS) reconstruction framework via a family of nonconvex nuclear norms functions which contain common concave and monotonically properties. To solve the resulting nonconvex nuclear norm minimization (NNM) problem, we develop a Group based iteratively double-reweighted nuclear norm algorithm (IDNN) via an alternating direction method of multipliers (ADMM) framework. Our proposed algorithm can convert the nonconvex nuclear norms optimization problem into a double-reweighted singular value thresholding (DSVT) problem. Extensive experiments demonstrate our proposed framework achieved favorable reconstruction performance compared with current state-of-the-art convex methods.