A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. I will deliver a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness.

This presentation is part of Minisymposium “MS42 - Low dimensional structures in imaging science (3 parts)”
organized by: Wenjing Liao (Georgia Institute of Technology) , Haizhao Yang (Duke University) , Zhizhen Zhao (University of Illinois Urbana-Champaign) .

Authors:

Samuel Vaiter (IMB, Université de Bourgogne)

Keywords:

inverse problems, nonlinear optimization