Compressive sensing with a spherical microphone array

Abstract

A wave expansion method is proposed in this work, based on measurements with a spherical microphone array, and formulated in the framework provided by Compressive Sensing. The method promotes sparse solutions via ℓ1-norm minimization, so that the measured data are represented by few basis functions. This results in fine spatial resolution and accuracy. This publication covers the theoretical background of the method, including experimental results that illustrate some of the fundamental differences with the “conventional” least-squares approach. The proposed methodology is relevant for source localization, sound field reconstruction, and sound field analysis.

Sound field reconstruction using a spherical microphone array

“…), conveying an interesting prospect in further work. 14 The numerical and experimental results show that the method is accurate and robust. Its accuracy depends on the ill-conditioning of the specific reconstruction: In the forward problem, the resulting error for the entire sound field reconstruction (pressure, velocity, and intensity) is below 10%.…”

“…For sparse signals, the solution from the ' 1 is equivalent to the ' 0 (pseudonorm) minimization, but forming a convex optimization problem that can be solved efficiently via quadratic programming. 14,34 This approach is presented in a separate study, see Ref. 14.…”

“…Equation (19) corresponds to the least squares solution of the problem with Tikhonov regularization. 22,33 The right inverse is chosen because it is more efficient computationally for an underdetermined problem like the one addressed here ðL > MÞ, given the dimensions of the product G Although the ' 2 -norm solution is chosen in this work, there are alternative solutions, such as the ' 1 -norm, 14 that promote sparse solutions, i.e., few non-zero coefficients, implicitly acting as a regularization penalty. For sparse signals, the solution from the ' 1 is equivalent to the ' 0 (pseudonorm) minimization, but forming a convex optimization problem that can be solved efficiently via quadratic programming.…”

“…They make it possible to resolve waves traveling in any direction, whereas this is not necessarily the case for conventional planar arrays. 10,11 Spherical microphone arrays are widely used for sound source localization, [12][13][14] sound field reproduction-to capture sound fields that can be reproduced with an array of loudspeakers, [15][16][17][18] and sound field analysis and reconstruction. [19][20][21][22][23][24][25][26] The use of rigid spherical microphone arrays for reconstructing sound fields has been the subject of several studies, [20][21][22][23][24] which employ a spherical harmonic expansion to provide a full representation of the sound field (sound pressure, particle velocity, and sound intensity).…”

Joint Acoustic Localization and Dereverberation Through Plane Wave Decomposition and Sparse Regularization

“…The promotion of a sparse solution enables a precise estimate of the DOA of multiple sound sources with an increased resolution. A similar approach is proposed in [18] using the spherical harmonic decomposition method (SHDM), a method that is closely related to the PWDM. Here the SHDM is used to construct an over-complete dictionary that accounts for the presence of a rigid baffle of a spherical microphone array.…”