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

Jérôme Antoni (1)

1 LVA - Laboratoire Vibrations Acoustique

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. (C) 2012 Acoustical Society of America. {[}DOI:10.1121/1.3685484]

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Jérôme Antoni. A Bayesian approach to sound source reconstruction: Optimal basis, regularization, and focusing. Journal of the Acoustical Society of America, 2012, 131 (4, Part 1), pp.2873-2890. ⟨10.1121/1.3685484⟩. ⟨hal-00776324⟩