title: Multiple and single snapshot compressive beamforming.
abstract: For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction of arrival (DOA) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem by expressing the acoustic pressure at each sensor as a phase-lagged superposition of source amplitudes at all hypothetical DOAs. Regularizing with an ℓ1-norm constraint renders the problem solvable with convex optimization, and promoting sparsity gives high-resolution DOA maps. Here the sparse source distribution is derived using maximum a posteriori estimates for both single and multiple snapshots. CS does not require inversion of the data covariance matrix and thus works well even for a single snapshot where it gives higher resolution than conventional beamforming. For multiple snapshots, CS outperforms conventional high-resolution methods even with coherent arrivals and at low signal-to-noise ratio. The superior resolution of CS is demonstrated with vertical array data from the SWellEx96 experiment for coherent multi-paths.
authors.affiliation: Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92093-0238, USA.
authors.forename: Peter
authors.initials: P
authors.lastname: Gerstoft
authors.affiliation: Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby 2800, Denmark.
authors.forename: Angeliki
authors.initials: A
authors.lastname: Xenaki
authors.affiliation: Christian Doppler Lab, Institute of Telecommunications, TU Wien, Gusshausstrasse 25/389, 1040 Vienna, Austria.
authors.forename: Christoph F
authors.initials: CF
authors.lastname: Mecklenbräuker