Patch-Based Image Inpainting via Two-Stage Low Rank Approximation

To recover the corrupted pixels, traditional inpainting methods based on low-rank priors generally need to solve a convex optimization problem by an iterative singular value shrinkage algorithm. In this paper, we propose a simple method for image inpainting using low rank approximation, which avoids the time-consuming iterative shrinkage. Specifically, if similar patches of a corrupted image are identified and reshaped as vectors, then a patch matrix can be constructed by collecting these similar patch-vectors. Due to its columns being highly linearly correlated, this patch matrix is low-rank. Instead of using an iterative singular value shrinkage scheme, the proposed method utilizes low rank approximation with truncated singular values to derive a closed-form estimate for each patch matrix. Depending upon an observation that there exists a distinct gap in the singular spectrum of patch matrix, the rank of each patch matrix is empirically determined by a heuristic procedure. Inspired by the inpainting algorithms with component decomposition, a two-stage low rank approximation (TSLRA) scheme is designed to recover image structures and refine texture details of corrupted images. Experimental results on various inpainting tasks demonstrate that the proposed method is comparable and even superior to some state-of-the-art inpainting algorithms.