Total-variation approach and wavelet shrinkage for color-image denoising with inter-channel cross-correlations

By replacing the total-variation (TV) norm in the TV variational denoising model by the Besov norm defined with the orthonormal wavelet coefficients of an image, the TV variational model is converted into the LI variational model in the wavelet domain, and its solution is the classical wavelet shrinkage. The wavelet shrinkage denoising scheme works well for monochrome images; but its direct application to color images does not utilize cross-correlations among the three primary color channels, and hence in most cases it produces several noticeable artifacts as side effects. To utilize the inter-channel cross-correlations, this paper introduces the TV norms of color differences and color sums into the classical TV variational model. Moreover, this paper replaces all the TV norms by the Besov norms, and then derives new wavelet shrinkage for color-image denoising. Experimental simulations demonstrate that the utilization of inter-channel cross-correlations alleviates the side effects of denoising, and improves picture quality of denoised images, as well as we have expected.