On the Complementarity of Sparse L0 and CEL0 Regularized Loss Landscapes for DOA Estimation.

L0 sparse methods are not widespread in Direction-Of-Arrival (DOA) estimation yet, despite their potential superiority over classical methods in difficult scenarios. This comes from the difficulties encountered for global optimization on hill-climbing error surfaces. In this paper, we explore the loss landscapes of L0 and Continuous Exact L0 (CEL0) regularized problems in order to design a new optimization scheme. As expected, we observe that the recently introduced CEL0 penalty leads to an error surface with less local minima than the L0 one. This property explains the good behavior of the CEL0-regularized sparse DOA estimation problem for well-separated sources. Unfortunately, CEL0-regularized landscape enlarges L0-basins in the middle of close sources, and CEL0 methods are thus unable to resolve two close sources. Consequently, we propose to alternate between both error surfaces to increase the probability of reaching the global solution. Experiments show that the proposed approach offers better performance than existing ones, and particularly an enhanced resolution limit.

Automatic determination of the number of targets present when using the time reversal operator.

Acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources. The DORT method is a derivation of the time reversal process, which allows for focusing on multiple targets. An important step in this process is the determination of the number of targets or sources present. This is achieved by examining the eigenvalues of the time reversal operator (TRO). The number of significant eigenvalues is then chosen as the number of sources present. However, as mentioned in [N. Mordant, C. Prada, and M. Fink, J. Acoust. Soc. Am. 105, 2634-2642 (1999) and C. Prada, M. Tanter, and M. Fink, in Proceedings of the IEEE Symposium, 1997, pp. 679-683], factors such as low signal to noise ratio (SNR), small data sample, array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues. This paper proposes a robust method of automatically determining the number of targets even in the presence of a small number of snapshots. For white Gaussian noise, the profile of the ordered eigenvalues is seen to fit an exponential law. The observed eigenvalues are then compared to this model and a mismatch is detected between the observed profile and the noise-only model. The index of the mismatch gives the number of scatterers present.