Resolution enhancement of two-dimensional grid-free compressive beamforming

Abstract

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.

A panoramic continuous compressive beamformer with cuboid microphone arrays

“…The atomic norm and the atomic norm of P are respectively defined asandwhere inf denotes the infimum. is a convex relaxation of 11,18,20 .…”

“…(4) can denoise P ⭑ and thus obtain P . is the direct metric of source sparsity 11,18,20 . However, it is non-deterministic polynomial-time hard to solve Eq.…”

“…Establish the metricwhere |·| denotes the determinant of a matrix and is a regularization parameter. has the following properties under a certain condition 11,14,18 : (1) is on the order of as κ approaches 0 if , i.e., ; (2) is on the order of as κ approaches +∞, i.e., ; (3) Denote by the optimal variable when κ approaches 0. The smallest eigenvalues of are either 0 or approach 0, i.e., only eigenvalues are large.…”

A Ratio Model of L1/L2 Norm for Sound Source Identification

“…In this Monte Carlo simulation, the position of the sound source was random while the SNR was 30 dB. According to the references [ 29 , 30 , 31 ], we defined the average reconstruction error (ARE) and the average quantitative error (AQE) in Equations ( 20 ) and ( 21 ) apiece, where , N is the number of the equivalent sources.…”

Two-Dimensional Multiple-Snapshot Grid-Free Compressive Beamforming Using Alternating Direction Method of Multipliers

“…In 2015, Xenaki and Gerstoft [13] presented a one-dimensional grid-free compressive beamforming strategy for the measurements with linear microphone arrays based on the minimization of the atomic norm of source strength and the polynomial rooting method. In 2017-2018, the authors [14,15] presented a two-dimensional grid-free compressive beamforming strategy for the measurements with planar microphone arrays based on the minimization of the atomic norm of microphone pressure induced by sources and the matrix enhancement and matrix pencil method [16]. Both these strategies are based on the single-snapshot data model and thus suitable to identify the transient or the moving sources.…”