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Direction-of-Arrival Estimation through Exact Continuous l20-Norm Relaxation

Emmanuel Soubies 1 Adilson Chinatto 2 Pascal Larzabal 3 João Romano 2 Laure Blanc-Féraud 4
1 IRIT-SC - Signal et Communications
IRIT - Institut de recherche en informatique de Toulouse
4 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : On-grid based direction-of-arrival (DOA) estimation methods rely on the resolution of a difficult group-sparse optimization problem that involves the l20 pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the l20 term with a group minimax concave penalty with suitable parameters. This relaxation is more amenable to non-convex optimization algorithms as it is continuous and admits less local (not global) minimizers than the initial l20-regularized criteria. We then show on numerical simulations that the minimization of the proposed relaxation with an iteratively reweighted l21 algorithm leads to an improved performance over traditional approaches.
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Submitted on : Tuesday, December 8, 2020 - 5:33:23 PM
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Emmanuel Soubies, Adilson Chinatto, Pascal Larzabal, João Romano, Laure Blanc-Féraud. Direction-of-Arrival Estimation through Exact Continuous l20-Norm Relaxation. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2021, 28, pp.16-20. ⟨10.1109/LSP.2020.3042771⟩. ⟨hal-03047201⟩



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