Direction-of-Arrival Estimation Through Exact Continuous ℓ2,0-Norm Relaxation - Soubies, Emmanuel; Chinatto, Adilson; Larzabal, Pascal; Romano, Joao M. T.; Blanc-Feraud, Laure (IEEE signal processing letters, 2021)
On-grid based direction-of-arrival (DOA) estimation methods rely on the resolution of a difficult group-sparse optimization problem that involves the \ell _{2,0} pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the \ell _{2,0} 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 \ell _{2,0} -regularized criteria. We then show on numerical simulations that the minimization of the proposed relaxation with an iteratively reweighted \ell _{2,1} algorithm leads to an improved performance over traditional approaches.