A hybrid structural sparse model for image restoration

Structural sparse model (SSM) has achieved great success in various image inverse problems. However, most existing methods just use a single norm, i.e., 11- or 12-norm, to constrain sparse coefficients. Unfortunately, the soft thresholding associated with 11-norm inactivates small coefficients, and the Wiener filtering associated with 12-norm produces an over-smooth solution. Both of them are unfavorable for protecting image details. To cope with this problem, in this paper, we propose a novel hybrid structural sparse model (HSSM) for image restoration, which can preserve image details more effectively. Unlike typical methods, the proposed HSSM uses 11- and 12-norm to constrain sparse coefficients simultaneously, and a scaling factor, which indicates the importance of each coefficient, is introduced to adaptively control the degree of sparsity penalty for each coefficient. Applying the proposed HSSM to image restoration, a general HSSM-based image restoration scheme is established, and the restored image, sparse coefficients and scaling factors can be efficiently solved by using alternating minimization. Furthermore, we prove that the solution of HSSM achieves a compromise between the solutions of 12-norm-based SSM and 11-norm-based SSM. Experimental results on image denoising, deblurring, and deblocking demonstrate that the proposed HSSM-based restoration method can not only outperform many state-of-the-art model-based methods in both PSNR and SSIM, but also compete with recent superior deep learning-based methods.