Image Recovery via Multiscale Total Variation

Total Variation (TV) methods, introduced by L. Rudin and S. Osher a few years ago, are very e ective for the recovery of blocky, possibly discontinuous images, from noisy data. Unfortunately they are not so e ective for the recovery of textured regions. To improve this, recently, L. Rudin introduced a novel functional, the Multiscale Total Variation (MTV). The functional is designed so that it takes into account the interaction between scales. In this paper we shall present both theoretical and experimental justi cation of the method. We study the MTV functional and give some existence and uniqueness results for the PDE associated to the functional via the steepest descent method. Then we end by displaying some numerical experiments that show the e ectiveness of the method.