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

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 becausethe noise statistics in R, G, B channels can be very different for real noisyimages. In this paper, we propose a multi-channel (MC) optimization model forreal color image denoising under the weighted nuclear norm minimization (WNNM)framework. We concatenate the RGB patches to make use of the channelredundancy, and introduce a weight matrix to balance the data fidelity of thethree channels in consideration of their different noise statistics. Theproposed MC-WNNM model does not have an analytical solution. We reformulate itinto a linear equality-constrained problem and solve it with the alternatingdirection method of multipliers. Each alternative updating step has closed-formsolution and the convergence can be guaranteed. Extensive experiments on bothsynthetic and real noisy image datasets demonstrate the superiority of theproposed MC-WNNM over state-of-the-art denoising methods.