A Bayesian approach to sound source reconstruction: Optimal basis, regularization, and focusing

作者：Antoni Jerome^*

来源：Journal of the Acoustical Society of America, 2012, 131(4): 2873-2890.

DOI：10.1121/1.3685484

The reconstruction of acoustical sources from discrete field measurements is a difficult inverse problem that has been approached in different ways. Classical methods (beamforming, near-field acoustical holography, inverse boundary elements, wave superposition, equivalent sources, etc.) all consist-implicitly or explicitly-in interpolating the measurements onto some spatial functions whose propagation are known and in reconstructing the source field by retropropagation. This raises the fundamental question as whether, for a given source topology and array geometry, there exists an optimal interpolation basis which minimizes the reconstruction error. This paper provides a general answer to this question, by proceeding from a Bayesian formulation that is ideally suited to combining information of physical and probabilistic natures. The main findings are the followings: (1) The optimal basis functions are the M eigen-functions of a specific continuous-discrete propagation operator, with M being the number of microphones in the array. (2) The a priori inclusion of spatial information on the source field causes super-resolution according to a phenomenon coined "Bayesian focusing." (3) The approach is naturally endowed with an internal regularization mechanism and results in a robust regularization criterion with no more than one minimum. (4) It admits classical methods as particular cases.

• 出版日期2012-4