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

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

compressive synthetic aperture sonar imaging with distributed optimization

Synthetic aperture sonar (SAS) provides high-resolution acoustic imaging by processing coherently the backscattered acoustic signal recorded over consecutive pings. Traditionally, object detection and classification tasks rely on high-resolution seafloor mapping achieved with widebeam, broadband SAS systems. However, aspect- or frequency-specific information is crucial for improving the performance of automatic target recognition algorithms. For example, low frequencies can be partly transmitted through objects or penetrate the seafloor providing information about internal structure and buried objects, while multiple views provide information about the object's shape and dimensions. Sub-band and limited-view processing, though, degrades the SAS resolution. In this paper, SAS imaging is formulated as an l1-norm regularized least-squares optimization problem which improves the resolution by promoting a parsimonious representation of the data. The optimization problem is solved in a distributed and computationally efficient way with an algorithm based on the alternating direction method of multipliers. The resulting SAS image is the consensus outcome of collaborative filtering of the data from each ping. The potential of the proposed method for high-resolution, narrowband, and limited-aspect SAS imaging is demonstrated with simulated and experimental data.Synthetic aperture sonar (SAS) provides high-resolution acoustic imaging by processing coherently the backscattered acoustic signal recorded over consecutive pings. Traditionally, object detection and classification tasks rely on high-resolution seafloor mapping achieved with widebeam, broadband SAS systems. However, aspect- or frequency-specific information is crucial for improving the performance of automatic target recognition algorithms. For example, low frequencies can be partly transmitted through objects or penetrate the seafloor providing information about internal structure and buried objects, while multiple views provide information about the object's shape and dimensions. Sub-band and limited-view processing, though, degrades the SAS resolution. In this paper, SAS imaging is formulated as an l1-norm regularized least-squares optimization problem which improves the resolution by promoting a parsimonious representation of the data. The optimization problem is solved in a distributed and computati..

Block-sparse beamforming for spatially extended sources in a Bayesian formulation

Direction-of-arrival (DOA) estimation refers to the localization of sound sources on an angular grid from noisy measurements of the associated wavefield with an array of sensors. For accurate localization, the number of angular look-directions is much larger than the number of sensors, hence, the problem is underdetermined and requires regularization. Traditional methods use an L2-norm regularizer, which promotes minimum-power (smooth) solutions, while regularizing with L1-norm promotes sparsity. Sparse signal reconstruction improves the resolution in DOA estimation in the presence of a few point sources, but cannot capture spatially extended sources. The DOA estimation problem is formulated in a Bayesian framework where regularization is imposed through prior information on the source spatial distribution which is then reconstructed as the maximum a posteriori estimate. A composite prior is introduced, which simultaneously promotes a piecewise constant profile and sparsity in the solution. Simulations and experimental measurements show that this choice of regularization provides high-resolution DOA estimation in a general framework, i.e., in the presence of spatially extended sources