  Patch-based sparse representation modeling has shown great potential in image
compressive sensing (CS) reconstruction. However, this model usually suffers
from some limits, such as dictionary learning with great computational
complexity, neglecting the relationship among similar patches. In this paper, a
group-based sparse representation method with non-convex regularization
(GSR-NCR) for image CS reconstruction is proposed. In GSR-NCR, the local
sparsity and nonlocal self-similarity of images is simultaneously considered in
a unified framework. Different from the previous methods based on
sparsity-promoting convex regularization, we extend the non-convex weighted Lp
(0 < p < 1) penalty function on group sparse coefficients of the data matrix,
rather than conventional L1-based regularization. To reduce the computational
complexity, instead of learning the dictionary with a high computational
complexity from natural images, we learn the principle component analysis (PCA)
based dictionary for each group. Moreover, to make the proposed scheme
tractable and robust, we have developed an efficient iterative
shrinkage/thresholding algorithm to solve the non-convex optimization problem.
Experimental results demonstrate that the proposed method outperforms many
state-of-the-art techniques for image CS reconstruction.
