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

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...

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Bibliographic Details
Published inIEEE signal processing letters Vol. 28; pp. 16 - 20
Main Authors Soubies, Emmanuel, Chinatto, Adilson, Larzabal, Pascal, Romano, João M T, Blanc-Féraud, Laure
Format Journal Article
LanguageEnglish
Published Institute of Electrical and Electronics Engineers 2021
Subjects
Engineering Sciences
Signal and Image processing
Exact relaxations
MMV-sparse optimization
DOA
l20-norm minimization
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Summary: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.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2020.3042771