Nonlinear L \(^2\) -DiracVTV Model for Color Image Restoration

Variational models for inverse problems are mainly based on the choice of the regularizer, whose goal is to give the solutions some desirable property. Vectorial Total Variation, one of the most popular regularizer for color image restoration, is induced by the Euclidean gradient operator. In this paper, we introduce a new regularizer for color image restoration, induced by a nonlinear extension of the Dirac operator to color images. Whereas the Vectorial Total Variation only promotes piece-wise constant solutions, the regularizer induced by the proposed Dirac operator also promotes solutions having the gradients of their color components aligned, which turns out to be a property of natural images. Then, we insert this regularizer into a variational model for image restoration, and we approximate its numerical solution by adapting the primal-dual algorithm of convex optimization. Experiments on denoising and deblurring show that the proposed Dirac operator provides a better regularizer than the Euclidean operator.