Multiple and single snapshot compressive beamforming

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 $\ell_1$-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 (MAP) 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.Comment: In press Journal of Acoustical Society of Americ

A Low-Cost Robust Distributed Linearly Constrained Beamformer for Wireless Acoustic Sensor Networks with Arbitrary Topology

We propose a new robust distributed linearly constrained beamformer which utilizes a set of linear equality constraints to reduce the cross power spectral density matrix to a block-diagonal form. The proposed beamformer has a convenient objective function for use in arbitrary distributed network topologies while having identical performance to a centralized implementation. Moreover, the new optimization problem is robust to relative acoustic transfer function (RATF) estimation errors and to target activity detection (TAD) errors. Two variants of the proposed beamformer are presented and evaluated in the context of multi-microphone speech enhancement in a wireless acoustic sensor network, and are compared with other state-of-the-art distributed beamformers in terms of communication costs and robustness to RATF estimation errors and TAD errors

Parametric high resolution techniques for radio astronomical imaging

The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the imaging equation in the cases of non co-planar arrays and polarimetric measurements. Then we improve our parametric imaging techniques in terms of resolution and estimation accuracy. This is done by enhancing both the MVDR parametric imaging, introducing alternative dirty images and by introducing better power estimates based on least squares, with positive semi-definite constraints. We also discuss the use of robust Capon beamforming and semi-definite programming for solving the self-calibration problem. Additionally we provide statistical analysis of the bias of the MVDR beamformer for the case of moving array, which serves as a first step in analyzing iterative approaches such as CLEAN and the techniques proposed in this paper. Finally we demonstrate a full deconvolution process based on the parametric imaging techniques and show its improved resolution and sensitivity compared to the CLEAN method.Comment: To appear in IEEE Journal of Selected Topics in Signal Processing, Special issue on Signal Processing for Astronomy and space research. 30 page

Grid-free compressive beamforming

The direction-of-arrival (DOA) estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors, thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve high-resolution imaging. On a discrete angular grid, the CS reconstruction degrades due to basis mismatch when the DOAs do not coincide with the angular directions on the grid. To overcome this limitation, a continuous formulation of the DOA problem is employed and an optimization procedure is introduced, which promotes sparsity on a continuous optimization variable. The DOA estimation problem with infinitely many unknowns, i.e., source locations and amplitudes, is solved over a few optimization variables with semidefinite programming. The grid-free CS reconstruction provides high-resolution imaging even with non-uniform arrays, single-snapshot data and under noisy conditions as demonstrated on experimental towed array data.Comment: 14 pages, 8 figures, journal pape