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Several continuous non-convex relaxations of the l0 pseudo-norm have been proposed over the past. In this talk, considering the l0-regularized least-squares minimization problem (l2-l0), I will present theoretical results which allow to compare such relaxations from the perspective of their fidelity to the initial l2-l0 problem. I will exhibit necessary and sufficient conditions on separable penalties approximating the l0 pseudo-norm which ensure that the associated regularized least-squares functional preserves the global minimizers of the initial one and do not add new local minimizers. From these conditions, we get a class of penalties said to be exact regarding to their properties concerning the relaxed functional.
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) .