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

Alternating projections gridless covariance-based estimation for DOA

We present a gridless sparse iterative covariance-based estimation method based on alternating projections for direction-of-arrival (DOA) estimation. The gridless DOA estimation is formulated in the reconstruction of Toeplitz-structured low rank matrix, and is solved efficiently with alternating projections. The method improves resolution by achieving sparsity, deals with single-snapshot data and coherent arrivals, and, with co-prime arrays, estimates more DOAs than the number of sensors. We evaluate the proposed method using simulation results focusing on co-prime arrays.Comment: 5 pages, accepted by (ICASSP 2021) 2021 IEEE International Conference on Acoustics, Speech, and Signal Processin

Conditional Wasserstein generative adversarial networks applied to acoustic metamaterial design

This work presents a method for the reduction of the total scattering cross section (TSCS) for a planar configuration of cylinders by means of generative modeling and deep learning. Currently, the minimization of TSCS requires repeated forward modelling at considerable computer resources, whereas deep learning can do this more efficiently. The conditional Wasserstein generative adversarial networks (cWGANs) model is proposed for minimization of TSCS in two dimensions by combining Wasserstein generative adversarial networks with convolutional neural networks to simulate TSCS of configuration of rigid scatterers. The proposed cWGAN model is enhanced by adding to it a coordinate convolution (CoordConv) layer. For a given number of cylinders, the cWGAN model generates images of 2D configurations of cylinders that minimize the TSCS. The proposed generative model is illustrated with examples for planar uniform configurations of rigid cylinders