Restoration Guarantee of Image Inpainting via Low Rank Patch Matrix Completion
Jian-Feng Cai, Jae Kyu Choi, Jingyang Li, and Guojian Yin

TL;DR
This paper provides a theoretical guarantee for patch-based image inpainting by reformulating it as a low-rank matrix completion problem, establishing conditions under which accurate restoration is possible.
Contribution
It introduces a mathematical framework linking patch-based image inpainting to low-rank matrix completion, with proven guarantees under certain incoherence and sampling conditions.
Findings
Restoration guarantee holds when samples exceed r log^2(N)
Reformulation as structured low-rank matrix completion
Provides theoretical insights into patch-based image restoration
Abstract
In recent years, patch-based image restoration approaches have demonstrated superior performance compared to conventional variational methods. This paper delves into the mathematical foundations underlying patch-based image restoration methods, with a specific focus on establishing restoration guarantees for patch-based image inpainting, leveraging the assumption of self-similarity among patches. To accomplish this, we present a reformulation of the image inpainting problem as structured low-rank matrix completion, accomplished by grouping image patches with potential overlaps. By making certain incoherence assumptions, we establish a restoration guarantee, given that the number of samples exceeds the order of , where denotes the size of the image and represents the sum of ranks for each group of image patches. Through our rigorous mathematical analysis,…
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Taxonomy
TopicsImage and Signal Denoising Methods · Advanced Image Processing Techniques · Medical Image Segmentation Techniques
