From rank estimation to rank approximation : rank residual constraint for image restoration

In this paper, we propose a novel approach for the rank minimization problem, termed rank residual constraint (RRC). Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underlying low-rank matrix directly from the corrupted observation, we progressively approximate (approach) the underlying low-rank matrix via minimizing the rank residual. Through integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we apply it to image restoration tasks, including image denoising and image compression artifacts reduction. Toward this end, we first obtain a good reference of the original image groups by using the image NSS prior, and then the rank residual of the image groups between this reference and the degraded image is minimized to achieve a better estimate to the desired image. In this manner, both the reference and the estimated image in each iteration are improved gradually and jointly. Based on the group-based sparse representation model, we further provide a theoretical analysis on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC model outperforms many state-of-the-art schemes in both the objective and perceptual qualities.Ministry of Education (MOE)This work was supported in part by the NSFC under Grant 61571102, in part by the Applied Research Programs of Science and Technology, Sichuan, under Grant 2018JY0035, in part by the Ministry of Education, Singapore, through the Start-Up Grant, and in part by the Macau Science and Technology Development Fund, Macau SAR, under Grant SKL-IOTSC-2018-2020, Grant 077/2018/A2, and Grant 022/2017/A1. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Chia-Kai Liang