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Abstract 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.
Abstract Group sparsity has shown great potential in various low-level vision tasks (e.g, image denoising, deblurring and inpainting). In this paper, we propose a new prior model for image denoising via group sparsity residual constraint (GSRC). To enhance the performance of group sparse-based image denoising, the concept of group sparsity residual is proposed, and thus, the problem of image denoising is translated into one that reduces the group sparsity residual. To reduce the residual, we first obtain some good estimation of the group sparse coefficients of the original image by the first-pass estimation of noisy image, and then centralize the group sparse coefficients of noisy image to the estimation. Experimental results have demonstrated that the proposed method not only outperforms many state-of-the-art denoising methods such as BM3D and WNNM, but results in a faster speed.