Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction

TL;DR

This paper introduces QNMF, a novel quaternion-based regularization method that effectively captures inter-channel correlations for improved color image reconstruction, demonstrating superior performance across multiple low-level vision tasks.

Contribution

The paper proposes a new quaternion nuclear norm minus Frobenius norm minimization approach that leverages quaternion algebra to better model color image structures.

Findings

Achieves state-of-the-art results in denoising, deblurring, inpainting, and impulse noise removal.

Effectively captures RGB channel correlations using quaternion algebra.

Provides theoretical proofs ensuring mathematical validity.

Abstract

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.