  In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and
low rank matrix completion (MC) is studied. The problem is formulated as a
nonconvex regularized leat square optimization problems, in which the l0-norm
and the rank function are replaced by l1-norm and nuclear norm, and adding a
nonconvex penalty function respectively. An alternating minimization scheme is
developed, and the existence of a subsequence, which generate by the
alternating algorithm that converges to a critical point, is proved. The NSP,
RIP, and RIP condition for stable recovery guarantees also be analysed for the
nonconvex regularized CS and MC problems respectively. Finally, the performance
of the proposed method is demonstrated through experimental results.
