Nonconvex Nonsmooth Low-Rank Minimization for Generalized Image Compressed Sensing via Group Sparse Representation

by   Yunyi Li, et al.

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 L_2-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.


page 21

page 22

page 26

page 27


Generalized Rank Minimization based Group Sparse Coding for Low-level Image Restoration via Dictionary Learning

Recently, low-rank matrix recovery theory has been emerging as a signifi...

Nonconvex L_ 1/2-Regularized Nonlocal Self-similarity Denoiser for Compressive Sensing based CT Reconstruction

Compressive sensing (CS) based computed tomography (CT) image reconstruc...

Deep Unfolding of Iteratively Reweighted ADMM for Wireless RF Sensing

We address the detection of material defects, which are inside a layered...

A Comparative Study for the Weighted Nuclear Norm Minimization and Nuclear Norm Minimization

Nuclear norm minimization (NNM) tends to over-shrink the rank components...

Generalized Singular Value Thresholding

This work studies the Generalized Singular Value Thresholding (GSVT) ope...

Robust PCA via Nonconvex Rank Approximation

Numerous applications in data mining and machine learning require recove...

Compressive Sensing via Low-Rank Gaussian Mixture Models

We develop a new compressive sensing (CS) inversion algorithm by utilizi...

Please sign up or login with your details

Forgot password? Click here to reset