Non-Local Robust Quaternion Matrix Completion for Color Images and Videos Inpainting

TL;DR

This paper introduces a novel nonlocal self-similarity (NSS) prior scheme based on low-rank properties for color image and video inpainting, demonstrating superior performance over existing methods.

Contribution

It establishes a theoretical link between NSS and low-rank structures, and proposes a quaternion matrix completion algorithm leveraging this for improved inpainting results.

Findings

Achieves higher PSNR and SSIM in image inpainting.

Demonstrates superior visual quality over state-of-the-art methods.

Extends the approach to color video inpainting using quaternion tensors.

Abstract

The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for image processing. However, there is no theoretical analysis on its working principle in the literature. In this paper, we discover a potential causality between NSS and low-rank property of color images, which is also available to grey images. A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images. The numerical low-rank property of patched matrices is also rigorously proved. The NSS-based QMC algorithm computes an optimal low-rank approximation to the high-rank color image, resulting in high PSNR and SSIM measures and particularly the better visual quality. A new tensor NSS-based QMC method is also presented to solve the color video inpainting problem based on quaternion tensor representation. The numerical experiments on color images and videos indicate the advantages of NSS-based QMC over the state-of-the-art methods.