Multi-channel nuclear norm minus Frobenius norm minimization for color image denoising

Abstract

Color image denoising is frequently encountered in various image processing and computer vision tasks. One traditional strategy is to convert the RGB image to a less correlated color space and denoise each channel of the new space separately. However, such a strategy can not fully exploit the correlated information between channels and is inadequate to obtain satisfactory results. To address this issue, this paper proposes a new multi-channel optimization model for color image denoising under the nuclear norm minus Frobenius norm minimization framework. Specifically, based on the block-matching, the color image is decomposed into overlapping RGB patches. For each patch, we stack its similar neighbors to form the corresponding patch matrix. The proposed model is performed on the patch matrix to recover its noise-free version. During the recovery process, a) a weight matrix is introduced to fully utilize the noise difference between channels; b) the singular values are shrunk adaptively without additionally assigning weights. With them, the proposed model can achieve promising results while keeping simplicity. To solve the proposed model, an accurate and effective algorithm is built based on the alternating direction method of multipliers (ADMM) framework. The solution of each updating step can be analytically expressed in closed-from. Rigorous theoretical analysis proves that the solution sequences generated by the proposed algorithm converge to their respective stationary points. Experimental results on both synthetic and real noise data sets demonstrate the proposed model outperforms state-of-the-art models. MATLAB code is available at https://www.github.com/wangzhi-swu/MCNNFNM.