Denoising color images using regularization and "correlation terms"

The problem addressed in this work is restoration of images that have several channels of information. We have studied color images so far, but hopefully the ideas presented here apply to other types of images with more than one channel. The suggested method is to use a probabilistic scheme which proved rather useful for image restoration and to incorporate into it an additional term which results in a better correlation between the color bands in the restored image. Results obtained so far are good; typically, there is a reduction of 20 to 40% in the mean square error, compared to standard restoration carried out separately on each color band. The contributions suggested in this work are the introduction of "correlation terms," which augment "standard" regularization, and the process of choosing two regularization hyperparameters. Also, a relation between the algorithm suggested here and the recently introduced ideas of smoothing by diffusion in color space is explored.