Nonconvex Nonsmooth Low-Rank Minimization for Peneralized Image
Compressed Sensing via Group Sparse Representation
Abstract
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.