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

Real-time near-field acoustic holography (RT-NAH) is used to recover non-stationary sound sources using a planar microphone array. Direct propagation is described by the convolution of the wavenumber spectrum of the source under study with a known impulse response. The deconvolution operation is achieved by a singular value decomposition of the propagator and Tikhonov regularization is performed to stabilize the solution. The inverse problem has an innate ill-posed characteristic, and the regularization process is the key factor in obtaining acceptable results. The purpose of this paper is to present the instantaneous regularization process applied to RT-NAH method. Bayesian estimation of the regularization parameter is introduced from prior knowledge of the problem. The computation of the regularization parameter is updated for each block of constant time interval allowing one to take into account the fluctuating properties of the sound field. The superiority of Bayesian regularization, compared to state-of-the art methods, is observed numerically and experimentally for reconstruction of non-stationary sources. RT-NAH is also enhanced to allow the reconstruction of long signals. Updating the regularization parameter accordingly to the fluctuations of the SNR is revealed to be a necessary effort to reconstruct highly non-stationary sources.

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

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.

Patch near-field acoustic holography: regularized extension and statistically optimized methods.

The patch holography method allows one to make measurements on an extended structure using a small microphone array. Increased attention has been paid to the two techniques, which are quite different at first glance. One is to extrapolate the pressure field measured on the hologram plane while the other is to use statistically optimized processing. A singular value decomposition formulation of the latter is proposed in this paper. The similarity of the two techniques is shown here. Both use a convolution of the measured pressure patch to obtain a better estimate of the wavenumber spectrum backward propagated on the structure. By using the Morozov discrepancy principle to compute the regularization parameter, the two methods lead to very close results.

Forward propagation of time evolving acoustic pressure: formulation and investigation of the impulse response in time-wavenumber domain.

The aim of this work is to continuously provide the acoustic pressure field radiated from nonstationary sources. From the acquisition in the nearfield of the sources of a planar acoustic field which fluctuates in time, the method gives instantaneous sound field with respect to time by convolving wavenumber spectra with impulse response and then inverse Fourier transforming into space for each time step. The quality of reconstruction depends on the impulse response which is composed of investigated parameters as transition frequency and propagation distance. Sampling frequency also affects errors of the practically discrete impulse response used for calculation. To avoid aliasing, the impulse response is low-pass filtered with Chebyshev or Kaiser-Bessel filter. Another approach to implement the impulse response consists of applying an inverse Fourier transform to the theoretical transfer function for propagation. To estimate the performance of each processing method, a simulation test involving several source monopoles driven by nonstationary signals is executed. Some indicators are proposed to assess the accuracy of the temporal signals predicted in a forward plane. The results show that the use of a Kaiser-Bessel filter numerically implemented or that of the inverse Fourier transform can provide the most accurate instantaneous acoustic signals.