A New Low-Rank Learning Robust Quaternion Tensor Completion Method for Color Video Inpainting Problem and Fast Algorithms

TL;DR

This paper introduces a robust quaternion tensor completion model for color video inpainting that preserves color channel coupling and video evolution, offering efficient recovery with theoretical guarantees and superior results.

Contribution

It proposes a novel low-rank quaternion tensor completion model and a low-rank learning extension with fast algorithms and convergence guarantees for improved color video inpainting.

Findings

Successfully recovers color videos with high PSNR and SSIM.

Eliminates color contamination and maintains scene continuity.

Outperforms state-of-the-art algorithms in experiments.

Abstract

The color video inpainting problem is one of the most challenging problem in the modern imaging science. It aims to recover a color video from a small part of pixels that may contain noise. However, there are less of robust models that can simultaneously preserve the coupling of color channels and the evolution of color video frames. In this paper, we present a new robust quaternion tensor completion (RQTC) model to solve this challenging problem and derive the exact recovery theory. The main idea is to build a quaternion tensor optimization model to recover a low-rank quaternion tensor that represents the targeted color video and a sparse quaternion tensor that represents noise. This new model is very efficient to recover high dimensional data that satisfies the prior low-rank assumption. To solve the case without low-rank property, we introduce a new low-rank learning RQTC model, which rearranges similar patches classified by a quaternion learning method into smaller tensors satisfying the prior low-rank assumption. We also propose fast algorithms with global convergence guarantees. In numerical experiments, the proposed methods successfully recover color videos with eliminating color contamination and keeping the continuity of video scenery, and their solutions are of higher quality in terms of PSNR and SSIM values than the state-of-the-art algorithms.