• VePub Press
  • Events
  • Exact Solutions to Super Resolution on Semi-algebraic Domains in Higher Dimensions

We investigate the multi-dimensional super resolution (SR) problem on multi-dimensional semi-algebraic domains for various sampling schemes such as Fourier or moments. We present a new semidefinite programming (SDP) formulation of the l1 minimization in the space of Radon measures. While standard approaches have focused on SDP relaxations of the dual program (a popular approach is based on Gram matrix representations), this paper introduces an exact formulation of the primal l1 minimization exact recovery problem of SR that unleashes standard techniques (such as moment-sum-of-squares hierarchies) to overcome intrinsic limitations of previous works in the literature. Notably, we show that one can exactly solve the SR problem in dimension greater than 2 and for a large family of domains described by semi-algebraic sets. Joint work with Yohann de Castro (Dept. Math, Univ. Paris-Sud Orsay), Fabrice Gamboa (Inst. Math. Univ. Toulouse) and Jean Bernard Lasserre (LAAS-CNRS Univ. Toulouse).

Biography:

Didier Henrion is a CNRS “Directeur de Recherche” (senior researcher) at LAAS (Laboratory of Analysis and Architecture of Systems) in the research group MAC. He is also holding a secondary appointment as a Professor at the Department of Automatic Control of the Faculty of Electrical Engineering of the Czech Technical University in Prague. He received the “Diplôme d’Ingénieur” (Engineer’s Degree) and the “Diplôme d’Etudes Approfondies” (Masters’ Degree) with specialization in control from Institut National des Sciences Appliquées (INSA), Toulouse, France, in September 1994. From October 1994 to December 1995 he was a research assistant at Universidad Simón Bolívar, Caracas, Venezuela. From February 1996 to December 1998 he was a Ph.D. student at the Institute of Information Theory and Automation, Prague, Czech Republic. From October 1996 to August 1999 he was a Ph.D. student at LAAS-CNRS in Toulouse, France. He received the “Candidate of Sciences” (Ph.D.) degree from the Academy of Sciences of the Czech Republic in December 1998, the “Diplôme de Doctorat” (Ph.D. degree) from INSA, Toulouse, in October 1999, the “Diplôme d’Habilitation à Diriger des Recherches” (French Habilitation) degree from Université Paul Sabatier de Toulouse in December 2007, and the “Docent” (Czech Habilitation) degree from Czech Technical University in Prague in June 2008. In 2013, he was awarded the grade of Professor of Technical Cybernetics in the Czech Republic.

In 2004, he was awarded the Bronze Medal from CNRS, for his achievements in systems control theory. In 2005, he was awarded, jointly with Fredrik Kahl, the David Marr Prize for the best paper at the International Conference on Computer Vision. In 2011, upon recommendation by a committee of the French Académie des Sciences, he was awarded a scientific grant by the Simone and Cino del Duca Foundation of the Institut de France, on the topic of applied mathematics. In 2012, he was awarded, jointly with Jérôme Malick, the Charles Broyden prize for the best paper in the journal Optimization Methods and Sofware.