Compressive beamforming realizes the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources by solving an underdetermined system of equations relating microphone pressures to a source distribution via compressive sensing. The conventional method assumes DOAs of sources to lie on a grid. Its performance degrades due to basis mismatch when the assumption is not satisfied. To overcome this limitation for the measurement with plane microphone arrays, a two-dimensional grid-free compressive beamforming is developed. First, a continuum based atomic norm minimization is defined to denoise the measured pressure and thus obtain the pressure from sources. Next, a positive semidefinite programming is formulated to approximate the atomic norm minimization. Subsequently, a reasonably fast algorithm based on alternating direction method of multipliers is presented to solve the positive semidefinite programming. Finally, the matrix enhancement and matrix pencil method is introduced to process the obtained pressure and reconstruct the source distribution. Both simulations and experiments demonstrate that under certain conditions, the grid-free compressive beamforming can provide high-resolution and low-contamination imaging, allowing accurate and fast estimation of two-dimensional DOAs and quantification of source strengths, even with non-uniform arrays and noisy measurements.
The identification of acoustic sources in a three-dimensional (3D) domain based on measurements with an array of microphones is a challenging problem: it entails the estimation of the angular position of the sources (direction of arrival), distance relative to the array (range), and the quantification of the source amplitudes. A 3D source localization model using a rigid spherical microphone array with spherical wave propagation is proposed. In this study, sparse Bayesian learning is used to perform localization in 3D space and examine the use of principal component analysis to denoise the measurement data. The performance of the proposed method is examined numerically and experimentally, which is tested both in a free-field and in a reverberant environment. The numerical and experimental investigations demonstrate that the approach offers accurate localization in a 3D domain, resolving closely spaced sources and making it possible to identify sources located at different ranges.
Reconstructing the acoustic source distribution via imposing a sparsity constraint on a continuum, the atomic norm minimization (ANM) based grid-free compressive beamforming can eliminate the basis mismatch of conventional grid-based compressive beamforming. However, it works well only for sufficiently separated sources, which prohibits high resolution. The drawback arises because it uses an atomic norm to measure the source sparsity, while the atomic norm is not a direct sparse metric and its minimization is equivalent to the sparsity constraint only when the sources are sufficiently separated. This paper devotes itself to overcoming the drawback for the two-dimensional ANM based grid-free compressive beamforming. First, a sparse metric that can promote sparsity to a greater extent than the atomic norm is proposed. Then, using this metric a minimization problem is formulated and the majorization-minimization (MM) solving algorithm is introduced. MM iteratively conducts atomic norm minimization with a sound reweighting strategy, and therefore the developed method can be termed as iterative reweighted atomic norm minimization (IRANM). Both simulations and experiments demonstrate that whether a standard uniform rectangular array or a non-uniform array constituted by a small number of microphones is utilized, IRANM can overcome the drawback and thus enhance the resolution.
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