A panoramic continuous compressive beamformer with cuboid microphone arrays

Yang Yang,Zhongming Xu,Yongxiang Zhang,Yong-Xin Yang,Zhigang Chu

doi:10.1038/s41598-019-47845-7

Abstract

Compressive beamforming is a powerful approach for the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources. The conventional grid-based discrete compressive beamformer suffers from the basis mismatch conundrum. Its result degrades under the situation that sources fall off the grid. The existing continuous compressive beamformer with linear or planar microphone arrays can circumvent the conundrum, but work well only for sources in a local region. Here we develop a panoramic continuous compressive beamformer with cuboid microphone arrays based on an atomic norm minimization (ANM) and a matrix pencil and paring method. To solve the positive semidefinite programming equivalent to the ANM efficiently, we formulate a solving algorithm based on the alternating direction method of multipliers. We also present an iterative reweighted ANM to enhance sparsity and resolution. The beamformer is capable of estimating the DOAs and quantifying the strengths of acoustic sources panoramically and accurately, whether a standard uniform or a sparse cuboid microphone array is utilized.

Highlights

Compressive sensing[1,2,3] based beamforming is an emerging and powerful approach for the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources, which is called compressive beamforming[4,5]
(3) We enhance sparsity and resolution via an iterative reweighted atomic norm minimization (ANM) (IRANM). (4) We investigate the applicability of the beamformer to the sparse cuboid microphone arrays, which are constructed via randomly retaining microphones from the standard uniform cuboid microphone arrays
Sources whose elevation angels lie in [0°, 90°] are accurately identified. This demonstrates the necessity of developing the panoramic continuous compressive beamformer to realize the panoramic DOA estimation and strength quantification of acoustic sources

Summary

Introduction

Compressive sensing[1,2,3] based beamforming is an emerging and powerful approach for the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources, which is called compressive beamforming[4,5]. Based on the minimization of the atomic norm of source strength and the polynomial rooting method, Xenaki et al.[15] developed a one-dimensional single-snapshot continuous compressive beamformer for the measurement with linear microphone arrays. The authors[17,18,19,20] developed a two-dimensional single-snapshot continuous compressive beamformer for the measurement with rectangular microphone arrays based on the minimization of the atomic norm of microphone signal induced by sources and the matrix enhancement and matrix pencil method[21], and extended it to the multiple-snapshot case via the group atomic norm and the matrix pencil and pairing (MaPP) method[13,14]. The key contributions are as follows: (1) we develop a panoramic continuous compressive beamformer with cuboid microphone arrays under the multiple-snapshot data model. The source strengths are quantified based on the estimated DOAs and the obtained microphone signal from sources. (2) Based on alternating direction method of multipliers (ADMM)[22,23,24], we formulate a reasonably fast algorithm to solve the positive semidefinite programming. (3) We enhance sparsity and resolution via an iterative reweighted ANM (IRANM). (4) We investigate the applicability of the beamformer to the sparse cuboid microphone arrays, which are constructed via randomly retaining microphones from the standard uniform cuboid microphone arrays

Methods

Results

Conclusion