Iterative positioning of microphone arrays for acoustic imaging

Abstract

For the characterization of acoustic sources, a common approach is to retro-propagate the sound pressure measured with a microphone array, which is often performed through the resolution of an inverse problem. The ill-posed nature of this problem, as well as the limited number of measurements, are known to reduce the quality of the source reconstruction. A practical solution to these limitations is to increase the number of measurements with new array placements. However, finding the best array positions is not a straightforward process. The present paper tackles this issue by introducing a sequential approach that selects at each iteration the optimal array placement. The proposed approach builds on two features rooted in a Bayesian framework: an inverse method called “Bayesian focusing” and a Bayesian search criterion based on the Kullback-Leibler divergence. Simulations results for the characterization of a directive source are used to illustrate the performance of the approach. It is shown that for a fixed number of iterations, the proposed approach performs better than ones where the successive placements are randomly selected around the source, or others where the placements follow a deterministic spherical grid pattern.