IMAGE RECOVERY VIA TOTAL VARIATION MINIMIZATION AND RELATED PROBLEMS

We study here a classical image denoising technique introduced by L. R udin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we give results of e xistence and uniqueness and prove the link between the constrained min imization problem and the minimization of an associated Lagrangian fun ctional. Then we describe a relaxation method for computing the soluti on, and give a proof of convergence. After this, we explain why the TV -based model is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose is to handle the minimization of the minimum of several convex functiona ls. We propose for instance a variant of the original TV minimization problem that handles correctly some situations where TV fails.