Regularization for improving the deconvolution in real-time near-field acoustic holography

Abstract

Near-field acoustic holography is a measuring process for locating and characterizing stationary sound sources from measurements made by a microphone array in the near-field of the acoustic source plane. A technique called real-time near-field acoustic holography (RT-NAH) has been introduced to extend this method in the case of nonstationary sources. This technique is based on a formulation which describes the propagation of time-dependent sound pressure signals on a forward plane using a convolution product with an impulse response in the time-wavenumber domain. Thus the backward propagation of the pressure field is obtained by deconvolution. Taking the evanescent waves into account in RT-NAH improves the spatial resolution of the solution but makes the deconvolution problem "ill-posed" and often yields inappropriate solutions. The purpose of this paper is to focus on solving this deconvolution problem. Two deconvolution methods are compared: one uses a singular value decomposition and a standard Tikhonov regularization and the other one is based on optimum Wiener filtering. A simulation involving monopoles driven by nonstationary signals demonstrates, by means of objective indicators, the accuracy of the time-dependent reconstructed sound field. The results highlight the advantage of using regularization and particularly in the presence of measurement noise.

Near-field electromagnetic holography for high-resolution analysis of network interactions in neuronal tissue

“…NAH typically involves the use of planar arrays of microphones ( Paillasseur et al, 2011 ). For an implementation with electromagnetic sources from brain tissue the following precedented analogies ( Morgan, 2003 ) from other NEH implementations are helpful (see Table 1 ): Microphone arrays corresponded to microelectrode arrays.…”

Instantaneous Bayesian regularization applied to real-time near-field acoustic holography

“…Regularization methods have proved their efficiency to ensure the stability of the solution for standard NAH problems and non-stationary problems. [9][10][11] The use of time kernels has the advantage of making possible the instantaneous estimation of the source field on the surface of interest, however, these approaches suffer from the same issue: the regularization process does not take into account the fluctuation of the energy of the acoustic signals. Statistical properties of the sound field are time-dependent and the amount of regularization has to be variable as well.…”

Block-sparse beamforming for spatially extended sources in a Bayesian formulation

“…Regularization with the ' 2 -norm is also typical in near-field acoustical holography (NAH) methods for sound field reconstruction. 2,3 Since there are usually only a few sources, regularization with the ' 1 -norm 4,5 attracts increasing attention [6][7][8][9][10][11][12][13][14][15][16] as it provides high-resolution DOA reconstruction due to its sparsity promoting characteristics. In underwater acoustics, using multiple constraints to account for simultaneous characteristics of the solution as sparsity and smoothness (i.e., ' 1 -norm and ' 2 -norm) is shown to improve the resolution of shallow-water source localization with matched-field processing.…”