Denoising Color Images Using Regularization and "Correlation Terms"

used to estimate the ‘‘roughness’’ of a grey-level image, was replaced by a three-dimensional Laplacian, which also The problem addressed in this work is restoration of images that have several channels of information. We have studied incorporates between-channel smoothness. Also, the GCV color images so far, but hopefully the ideas presented here method for estimating the regularization parameter (see apply to other types of images with more than one channel. Section 4) was extended to handle multichannel regularThe suggested method is to use a probabilistic scheme which ization. proved rather useful for image restoration and to incorporate Our approach resembles that of [24]; however, we suginto it an additional term which results in a better correlation gest measuring the smoothness in color space by different between the color bands in the restored image. Results obtained methods. This is motivated by the observation that spatial so far are good; typically, there is a reduction of 20 to 40% in smoothness and ‘‘color smoothness’’ are, in our opinion, the mean square error, compared to standard restoration carrather different entities. For instance, an image can have ried out separately on each color band. The contributions suga very rough spatial structure, but be very smooth in color gested in this work are the introduction of ‘‘correlation terms,’’ which augment ‘‘standard’’ regularization, and the process of space, and vice versa. ‘‘Color smoothness’’ is naturally choosing two regularization hyperparameters. Also, a relation defined by the change in the chrominance, not the between the algorithm suggested here and the recently introbrightness. duced ideas of smoothing by diffusion in color space is The difference between spatial smoothness and color explored.  1998 Academic Press smoothness can be demonstrated by a simple example. Suppose P1 and P2 are adjacent pixels. In case (a), let the color values of P1 , in the red-green-blue (RGB in the