Mapping uncertainties involved in sound source reconstruction with a cross-spectral-matrix-based Gibbs sampler.

The reconstruction of sound sources by using inverse methods is known to be prone to estimation errors due to measurement noise, model mismatch, and poor conditioning of the inverse problem. This paper introduces a solution to map the estimation errors together with the reconstructed sound sources. From a Bayesian perspective, it initializes a Gibbs sampler with the Bayesian focusing method. The proposed Gibbs sampler is shown to converge within a few iterations, which makes it realistic for practical purposes. It also turns out to be very flexible in various scenarios. One peculiarity is the capability to directly operate on the cross-spectral matrix. Another one is to easily accommodate sparse priors. Eventually, it can also account for uncertainties in the microphone positions, which reinforces the regularization of the inverse problem.

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.