Uzawa Block Relaxation Methods for Color Image Restoration

Abstract

In this paper we propose to investigate the use of a vectorial total variation model with spatially varying regularization and data terms for color image denoising and restoration. We pay attention to two main minimization problems: the minimization of a weighted vectorial total variation term TVg, which acts as a regularization term, using the L2 norm as data term or the minimization of the vectorial total variation with a spatially varying $L^1_g$ norm. The optimization process takes benefit of convex optimization tools by introducing an augmented Lagrangian formulation. This formulation leads us to simple and efficient algorithms based on Uzawa block relaxation schemes that are also robust towards the choice of the penalty parameter. In this paper, We propose to study more particularly the impact of spatially varying terms (total variation term or data terms) for color image restoration. A new weighted total variation term is proposed for old parchments restoration and we also compare the use of a weighted total variation term with a spatially varying data term for impulse noise removal in color images.