Nonlocal Patch Based t-SVD for Image Inpainting: Algorithm and Error Analysis

Abstract

In this paper, we propose a novel image inpainting framework consisting of an interpolation step and a low-rank tensor completion step. More specifically, we first initial the image with triangulation-based linear interpolation, and then we find similar patches for each missing-entry centered patch. Treating a group of patch matrices as a tensor, we employ the recently proposed effective t-SVD tensor completion algorithm with a warm start strategy to inpaint it. We observe that the interpolation step is such a rough initialization that the similar patch we found may not exactly match with the reference, so we name the problem as Patch Mismatch and analyse the error caused by it thoroughly. Our theoretical analysis shows that the error caused by Patch Mismatch can be decomposed into two components, one of which can be bounded by a reasonable assumption named local patch similarity, and another part is lower than that using matrix. Experiments on real images verify our method's superiority to the state-of-the-art inpainting methods.