Nonlinear DIP-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. Total Variation, one of the most popular regularizer for image restoration, is induced by the Euclidean gradient operator and promotes piece-wise constant solutions. In this paper, we present a new regularizer for color image restoration, which is induced by a generalization of the Dirac operator. This new regularizer also encourages the gradients of the three color components of the solutions to be aligned, which is actually a property of natural images. This property is also encoded when the regularizer is induced by a Riemannian gradient, for a well-chosen Riemannian metric, but with a different mathematical formulation. Then, we compare the different regularizers by combining them with the Deep Image Prior model, this latter assuming that the restored image is the output of a neural network. Experiments on denoising and deblurring show that the proposed Dirac operator provides better results than the Euclidean and Riemannian gradient operators.