Total variation image restoration: Overview and recent developments

Since their introduction in a classic paper by Rudin, Osher and Fatemi [695], total variation minimizing models have become one of the most popular and successful methodology for image restoration. More recently, there has been a resurgence of interest and exciting new developments, some extending the applicabilities to impainting, blind deconvolution and vector-valued images, while others offer improvements in better preservation of contrast, geometry and textures, in ameliorating the staircasing effect, and in exploiting the multiscale nature of the models. In addition, new computational methods have been proposed with improved computational speed and robustness. We shall review some of these recent developments.