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.