Bayesian identification of sound sources with the Helmholtz equation
For researchers in acoustics and inverse problems, this provides a Bayesian framework with theoretical guarantees for source identification, though it is an incremental extension of existing Bayesian methods to a specific PDE model.
The paper tackles the problem of identifying sound sources from noisy pressure measurements using a Bayesian approach with the Helmholtz equation. It proposes a problem-specific prior and algorithms for posterior approximation, proving convergence rates of the discretized posterior, with numerical experiments confirming sharp rates.
In this work we discuss the problem of identifying sound sources from pressure measurements with a Bayesian approach. The acoustics are modelled by the Helmholtz equation and the goal is to get information about the 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 resulting discretized posterior to the true posterior. The theoretical results are illustrated by numerical experiments, which indicate that the proven rates are sharp.