Efficient Schemes in Nonsmooth and Nonconvex Minimization

Optimization plays a central role in modern image processing. While convex optimization has received considerable interest in the field, nonsmooth nonconvex optimization remains much less developed. Yet, there are many problems in image processing that involve nonconvex and nonsmooth functionals to minimize, e.g. in approximation theory and compressed sensing. The goal of this minisymposium is to bring together recognized experts in optimization theory and image processing, to exhibit different approaches to solve nonsmooth and nonconex optimization problems. We will focus primarily on deterministic approaches and compare the performances as well as the limits of the methods proposed by the invited speakers.

Organizer: Jalal Fadili
Université de Caen, France
Mila Nikolova
ENS Cachan, France

Part I of II

9:30-9:55 Lower Semi-Continuity of Non-Local Functionals

Peter Elbau, Johann Radon Institute for Computational and Applied Mathematics, Austria

10:00-10:25 Sparse Regularization with Non-convex Regularization Terms

Markus Grasmair, Universität Innsbruck, Austria

10:30-10:55 Convex Relaxations of Metrics for Imaging with Missing Data

Russell Luke, University of Delaware

Part II of II

2:00-2:25 Optimization with Total Generalized Variation Penalty

Kristian Bredies, University of Bremen, Germany

2:30-2:55 DC (Difference of Convex functions) Programming and DCA (DC Algorithms) for Smooth/ Nonsmooth Nonconvex Programming

Tao Pham Dinh, National Institute for Applied Sciences, Rouen, France

3:00-3:25 DC Programming Approaches for Image Restoration and Image Segmentation

Hoai An Le Thi, Université Paul Verlaine, France

3:30-3:55 Linear Convergence Method for a Non-convex Variational Model

Tieyong Zeng and Michael Ng, Hong Kong Baptist University, Hong Kong