Alternating structure-adapted proximal gradient descent (ASAP) for nonconvex nonsmooth regularised problems with smooth coupling terms. Applications in imaging problemsMS37

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) .

Mila Nikolova (CMLA - CNRS ENS Cachan, University Paris-Saclay)
Pauline Tan (CMLA, École normale supérieure Paris-Saclay)
alternating minimization, computer vision, image deblurring, image reconstruction, inverse problems, kurdyka-lojasiewicz property, nonconvex-nonsmooth minimization, nonlinear optimization, subanalytic functions