Constrained low-rank quaternion approximation for color image denoising by bilateral random projections

TL;DR

This paper introduces a low-rank quaternion approximation model for color image denoising that leverages the correlation among RGB channels and employs quaternion bilateral random projections for efficient optimization, demonstrating superior denoising performance.

Contribution

It proposes a novel low-rank quaternion approximation model constrained by quaternion rank prior, utilizing quaternion bilateral random projections for efficient optimization in color image denoising.

Findings

Effective noise removal in color images.

Outperforms existing denoising methods.

Utilizes quaternion-based approach for holistic color processing.

Abstract

In this letter, we propose a novel low-rank quaternion approximation (LRQA) model by directly constraining the quaternion rank prior for effectively removing the noise in color images. The LRQA model treats the color image holistically rather than independently for the color space components, thus it can fully utilize the high correlation among RGB channels. We design an iterative algorithm by using quaternion bilateral random projections (Q-BRP) to efficiently optimize the proposed model. The main advantage of Q-BRP is that the approximation of the low-rank quaternion matrix can be obtained quite accurately in an inexpensive way. Furthermore, color image denoising is further based on nonlocal self-similarity (NSS) prior. The experimental results on color image denoising illustrate the effectiveness and superiority of the proposed method.