There is an increasing interest in block regularized nonconvex nonsmooth optimization. We introduce an approach that effectively exploits the structure of the problem and enables complex application-dependent regularization to be used. The proposed ASAP algorithm enjoys simple explicit updates. Global convergence to a critical point is proved using the Kurdyka-Lojasiewicz property. We also prove that a large class of useful objective functions satisfy this property. Applications of ASAP to various imaging problems are presented.

This presentation is part of Minisymposium “MS37 - Sparse-based techniques in variational image processing (2 parts)”
organized by: Serena Morigi (Dept. Mathematics, University of Bologna) , Ivan Selesnick (New York University) , Alessandro Lanza (Dept. Mathematics, University of Bologna) .

Authors:

Mila Nikolova (CMLA - CNRS ENS Cachan, University Paris-Saclay)

Pauline Tan (CMLA, École normale supérieure Paris-Saclay)

Keywords:

alternating minimization, computer vision, image deblurring, image reconstruction, inverse problems, kurdyka-lojasiewicz property, nonconvex-nonsmooth minimization, nonlinear optimization, subanalytic functions