Title: An off-the-grid method for the recovery of piecewise constant images in linear inverse problems
Authors: Vincent Duval - INRIA Paris (France)
Romain Petit - INRIA Paris and Paris-Dauphine University (France) [presenting]
Yohann De Castro - Ecole Centrale Lyon (France)
Abstract: In recent years, off-the-grid methods have drawn a lot of attention in the statistics and image processing community because of their improved robustness and statistical guarantees compared to their grid-based counterparts. We will describe a method to perform the recovery of piecewise constant (``cartoon'') images, using the (gradient) total variation prior, in the spirit of the Rudin-Osher-Fatemi model. By exploiting the properties of the faces of the level sets of the regularizer and by relying on the Frank-Wolfe algorithm we propose a method that does not rely on a predefined grid, but adapts to the geometry of the unknown.