Group
sparse representation (GSR) based method has led to great successes in various image
recovery tasks, which can be converted into a low-rank matrix minimization
problem. As a widely used surrogate function of low-rank, the nuclear norm
based convex surrogate usually leads to over-shrinking problem, since the standard
soft-thresholding operator shrinks all singular values equally. To improve traditional
sparse representation based image compressive sensing (CS) performance, we
propose a generalized CS framework based on GSR model, leading to a nonconvex
nonsmooth low-rank minimization problem. The popular
-norm
and M-estimator are employed for standard image CS and robust CS problem to fit
the data respectively. For the better approximation of the rank of group-matrix,
a family of nuclear norms are employed to address the over-shrinking problem. Moreover,
we also propose a flexible and effective iteratively-weighting strategy to control
the weighting and contribution of each singular value. Then we develop an iteratively
reweighted nuclear norm algorithm for our generalized framework via an
alternating direction method of multipliers framework, namely, GSR-ADMM-IRNN. Experimental
results demonstrate that our proposed CS framework can achieve favorable reconstruction
performance compared with current state-of-the-art methods and the RCS
framework can suppress the outliers effectively.
Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm