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

Shenghai Liao, Shujun Fu, Yuliang Li and Hongbin Han

Applied Mathematics and Computation, 2023, vol. 452, issue C

Abstract: 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.

Keywords: Low rank decomposition; Image inpainting; Inverse problem; Multidirectional search; Matrix completion (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:452:y:2023:i:c:s0096300323002175

DOI: 10.1016/j.amc.2023.128048

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