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Séminaires IRIT-UPS



Exact continuous relaxations for the l0-regularized least-squares criteria

Emmanuel SOUBIES - École Polytechnique Fédérale de Lausanne (EPFL) (Suisse)

Jeudi 19 Octobre 2017, 16h30 - 17h30
INP-ENSEEIHT, Salle des thèses
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Several continuous non-convex relaxations of the l0 pseudo-norm have been proposed over the past. However, the choice of one relaxation rather than another one remains unclear. 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. Then, I will focus on the inferior limit of this class which has special properties and is the one which removes the largest number of minimizers of the initial criteria. Finally, I will present concrete applications for different inverse problems such as single molecule localization microscopie (SMLM) and direction of arrival estimation in array processing.

Short Bio: Emmanuel Soubies received the PhD degree in signal and image processing from the University of Nice in 2016. He is currently a Post-Doc in the Biomedical Imaging Group at EPFL. His main research interests are inverse problems for imaging and sparse optimization.