Compressed sensing image reconstruction via adaptive sparse nonlocal regularization

Compressed sensing (CS) has been successfully utilized by many computer vision applications. However,the task of signal reconstruction is still challenging, especially when we only have the CS measurements of an image (CS image reconstruction). Compared with the task of traditional image restoration (e.g., image denosing, debluring and inpainting, etc.), CS image reconstruction has partly structure or local features. It is difficult to build a dictionary for CS image reconstruction from itself. Few studies have shown promising reconstruction performance since most of the existing methods employed a fixed set of bases (e.g., wavelets, DCT, and gradient spaces) as the dictionary, which lack the adaptivity to fit image local structures. In this paper, we propose an adaptive sparse nonlocal regularization (ASNR) approach for CS image reconstruction. In ASNR, an effective self-adaptive learning dictionary is used to greatly reduce artifacts and the loss of fine details. The dictionary is compact and learned from the reconstructed image itself rather than natural image dataset. Furthermore, the image sparse nonlocal (or nonlocal self-similarity) priors are integrated into the regularization term, thus ASNR can effectively enhance the quality of the CS image reconstruction. To improve the computational efficiency of the ASNR, the split Bregman iteration based technique is also developed, which can exhibit better convergence performance than iterative shrinkage/thresholding method. Extensive experimental results demonstrate that the proposed ASNR method can effectively reconstruct fine structures and suppress visual artifacts, outperforming state-of-the-art performance in terms of both the PSNR and visual measurements.