Advances in Nonsmooth and Nonconvex Minimization for Imaging

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 inverse problems. The minisymposium will give an overview of recent advances on both theoretical and algorithmic aspects of minimizing nonsmooth nonconvex objective functionals. Topics that will be covered range from well-posedness, to characterization of the minimizers and algorithms to reach them. The minisymposium will bring together recognized experts in optimization theory and imaging sciences.

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

Part I of II

9:30-9:55 Nonconvex, Nonsmooth Optimization via Gradient Sampling
Frank E. Curtis, Lehigh University, USA
10:00-10:25 On the Evaluation Complexity of Nonsmooth Composite Function Minimization with Applications to Nonconvex Nonlinear Programming
Coralia Cartis, University of Edinburgh, United Kingdom
10:30-10:55 High-Dimensional Covariance Estimation under Sparse Kronecker Product Structure
Alfred O. Hero, The University of Michigan, Ann Arbor, USA
11:00-11:25 Wasserstein Barycenter: Global Minimizers and Algorithm
Rabin Julien, CNRS-Université, France

Part II of II

2:00-2:25 On Local Linear Convergence of Elementary Algorithms with Sparsity Constraints
Russell Luke, University of Goettingen, Germany
2:30-2:55 L1 Data Fitting with Concave Regularization for Image Recovery
Mila Nikolova, ENS Cachan, France
3:00-3:25 Sparse Approximation via Penalty Decomposition Methods
Zhaosong Lu, Simon Fraser University, Canada
3:30-3:55 Symbology-based Algorithms for Robust Bar Code Recovery
Rachel Ward, University of Texas at Austin, USA