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 ‘1-norm constraint
renders the problem solvable with convex optimization, and promoting sparsity gives highresolution
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.
Original language | English |
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Journal | Journal of the Acoustical Society of America |
Volume | 138 |
Issue number | 4 |
Pages (from-to) | 2003–2014 |
ISSN | 0001-4966 |
DOIs | |
Publication status | Published - 2015 |