Image inpainting using non-convex low rank decomposition and multidirectional search

Low-rank (LR) and nonlocal self-similarity (NSS) are two important priors for image inpainting as a typical inverse problem. Nuclear norm minimization (NNM) is a widely used convex relaxation for relevant rank minimization problems. However, NNM regularizes each singular value equally and ignores the significance of bigger singular values. In this paper, we propose a non-convex low-rank decomposition (NC-LRD) model that is based on robust principal component analysis (RPCA) with a weighted L1 norm. Utilizing NSS prior for image inpainting we search similar patches by using a newly designed multidirectional search (MS) method, and apply the NC-LRD model to complete each corrupted patch matrix (low-rank decomposition with multidirectional search, MS-LRD). We focus on the spatial distribution of similar patches by restricting matched N patches to locate at N different directions relative to a target patch, while previous state-of-the-art methods do not consider the spatial distribution in similarity criterion. The MS method solves the problem that many patch-based inpainting algorithms fail to complete missing lines. Experimental results on line missing demonstrate that the proposed NC-LRD method has lower reconstruction error in matrix completion, and it converges faster than several state-of-the-art matrix completion algorithms. At the same time, the effectiveness and superiority of MS-LRD over other competitive inpainting algorithms are also verified.