Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising

TL;DR

This paper introduces a multi-channel weighted nuclear norm minimization model for effective real color image denoising, addressing the challenge of different noise statistics across RGB channels.

Contribution

It extends nuclear norm minimization to color images by incorporating channel-specific weights and a novel optimization approach, improving denoising performance.

Findings

Outperforms state-of-the-art denoising methods on synthetic datasets.

Effectively handles real noisy images with diverse noise characteristics.

Converges reliably with closed-form solutions in each iteration.

Abstract

Most of the existing denoising algorithms are developed for grayscale images, while it is not a trivial work to extend them for color image denoising because the noise statistics in R, G, B channels can be very different for real noisy images. In this paper, we propose a multi-channel (MC) optimization model for real color image denoising under the weighted nuclear norm minimization (WNNM) framework. We concatenate the RGB patches to make use of the channel redundancy, and introduce a weight matrix to balance the data fidelity of the three channels in consideration of their different noise statistics. The proposed MC-WNNM model does not have an analytical solution. We reformulate it into a linear equality-constrained problem and solve it with the alternating direction method of multipliers. Each alternative updating step has closed-form solution and the convergence can be guaranteed. Extensive experiments on both synthetic and real noisy image datasets demonstrate the superiority of the proposed MC-WNNM over state-of-the-art denoising methods.