Bayesian identification of sound sources with the Helmholtz equation

Sebastian Engel, Dominik Hafemeyer, Christian Münch, Daniel Schaden

Published 2018-05-29Version 1

In this work we discuss the problem of identifying sound sources with a Bayesian approach. The acoustics are modelled by the Helmholtz equation and the goal is to get information about number, strength and position of the sound sources, under the assumption that measurements of the acoustic pressure are noisy. We propose a problem specific prior distribution of the number, the amplitudes and positions of the sound sources and algorithms to compute an approximation of the associated posterior. We also discuss a finite element discretization of the Helmholtz equation for the practical computation and prove convergence rates of the discretized posterior to the true posterior. The theoretical results are illustrated by numerical experiments.