Tony Chan

Title: TVL1 models for imaging: global optimization and geometric properties: Part I 

Abstract: Rudin, Osher, and Fatemi's total variation based image denoising model has been very popular. We describe properties of a variant in which the fidelity term is replaced by the L1 norm. This seemingly modest modification has important consequences, in terms of contrast invariance, multiscale image decompositions, and geometric properties of solutions. In addition, it has connections to convex formulations of certain important shape optimization problems from computer vision, such as shape denoising and piecewise constant segmentation. In particular, we show that it leads to algorithms based on convex optimization techniques that are guaranteed to find the global minimizer of certain non-convex shape optimization problems.