Multichannel Color Image Denoising via Weighted Schatten p-norm Minimization

The R, G and B channels of a color image generally have different noise statistical properties or noise strengths. It is thus problematic to apply grayscale image denoising algorithms to color image denoising. In this paper, based on the non-local self-similarity of an image and the different noise strength across each channel, we propose a Multi-Channel Weighted Schatten p-Norm Minimization (MCWSNM) model for RGB color image denoising. More specifically, considering a small local RGB patch in a noisy image, we first find its nonlocal similar cubic patches in a search window with an appropriate size. These similar cubic patches are then vectorized and grouped to construct a noisy low-rank matrix, which can be recovered using the Schatten p-norm minimization framework. Moreover, a weight matrix is introduced to balance each channel's contribution to the final denoising results. The proposed MCWSNM can be solved via the alternating direction method of multipliers. Convergence property of the proposed method are also theoretically analyzed. Experiments conducted on both synthetic and real noisy color image datasets demonstrate highly competitive denoising performance, outperforming comparison algorithms, including several methods based on neural networks.