Single and multiple snapshot compressive beamforming by Peter Gerstoft, Angeliki Xenaki, Christoph F. Mecklenbräuker
For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction-of-arrivals (DOAs) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem expressing the acoustic pressure at each sensor as a phase-lagged superposition of source amplitudes at all hypothetical DOAs. Regularizing with an $\ell_1$-norm constraint renders the problem solvable with convex optimization, while promoting sparsity resulting in 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 resulting in 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.
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