Low Rank Quaternion Matrix Completion Based on Quaternion QR Decomposition and Sparse Regularizer

TL;DR

This paper introduces a low-rank quaternion matrix completion method using quaternion QR decomposition and sparse regularization, improving computational efficiency and performance in color image recovery.

Contribution

It proposes a novel quaternion QR-based approximate SVD method (CQSVD-QQR) and integrates it into a low-rank sparse regularized quaternion matrix completion framework.

Findings

Outperforms state-of-the-art methods on color image datasets

Reduces computational complexity compared to traditional QSVD-based methods

Effectively recovers color images and medical images with high accuracy

Abstract

Matrix completion is one of the most challenging problems in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. Because it treats the color image as a whole, the coupling information between the three channels of the color image is better utilized. Due to this, low-rank quaternion matrix completion (LRQMC) algorithms have gained considerable attention from researchers. In contrast to the traditional quaternion matrix completion algorithms based on quaternion singular value decomposition (QSVD), we propose a novel method based on quaternion Qatar Riyal decomposition (QQR). In the first part of the paper, a novel method for calculating an approximate QSVD based on iterative QQR is proposed (CQSVD-QQR), whose computational complexity is lower than that of QSVD. The largest $r \ (r>0)$ singular values of a given quaternion matrix can be computed by using CQSVD-QQR. Then, we propose a new quaternion matrix completion method based on CQSVD-QQR which combines low-rank and sparse priors of color images. Experimental results on color images and color medical images demonstrate that our model outperforms those state-of-the-art methods.