Bayesian Approach in Acoustic Source Localization and Imaging
Ning Chu, Laboratoire des signaux et systèmes (l2s), SUPELEC, France

Seminar • 23 December 2013 • BM 4.233

Abstract
Acoustic imaging is an advanced technique for acoustic source localization and power reconstruction using limited measurements at microphone sensor array. This technique can provide meaningful insights into performances, properties and mechanisms of acoustic sources. It has been widely used for evaluating the acoustic comfort in automobile and aircraft industries. Acoustic imaging methods often involve in two aspects: a forward model of acoustic signal (power) propagation, and its inverse solution. However, the inversion usually causes a very ill-posed inverse problem, whose solution is not unique and is quite sensitive to measurement errors. Therefore, classical methods cannot easily obtain high spatial resolutions between two close sources, nor achieve wide dynamic range of acoustic source powers. In this thesis, we firstly build up a discrete forward model of acoustic signal propagation. This signal model is a linear but underdetermined system of equations linking the measured data and unknown source signals and positions. Based on this signal model, we set up a discrete forward model of acoustic power propagation. This power model is both linear and determined. It can directly reflect the relationship between the measurements and source powers. In the forward models, we consider the measurement errors to be mainly composed of background noises at sensor array, model uncertainty caused by multi-path propagation, as well as model approximating errors. For the inverse problem of the acoustic power model, we firstly propose a robust super-resolution approach with the sparsity constraint, so that we can obtain very high spatial resolution in strong measurement errors. But the sparsity parameter should be carefully estimated for effective performance. Then for the acoustic imaging with large dynamic range and super resolution, we propose a robust Bayesian inference approach with a sparsity enforcing prior. This sparse prior can better embody the sparsity characteristic of source distribution than the sparsity constraint. All the unknown variables and parameters can be automatically estimated by the Joint Maximum A Posterior (JMAP) estimation. However, this JMAP confronts a non-quadratic optimization and causes huge computational cost. In order to accelerate the JMAP estimation, we investigate an invariant 2D convolution operator to approximate acoustic power propagation model. Furthermore, we consider more practical cases: the measurement errors are spatially variant (non-stationary) at different senors, rather than the ideal Gaussian white one. The sparsity enforcing distribution can be more accurately modeled by the Student's-t priors. In these cases, the JMAP confronts more limitations than advantages. Therefore, we apply the Variational Bayesian Approximation (VBA) to overcome the drawbacks of the JMAP. Above all, proposed approaches are validated by simulations, real data from wind tunnel experiments of Renault S2A, as well as the hybrid data. Compared with some typical state-of-the-art methods, the main advantages of proposed approaches are robust to measurement errors, super spatial resolutions, wide dynamic range and no need for source number or Signal to Noise Ration (SNR) beforehand.