  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.
