Deterministic-statistical approach for an inverse acoustic source problem using multiple frequency limited aperture data

Abstract

<p>We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the source. The Dirichlet eigenfunctions of the disc are used to expand the source function. Then the inverse problem is recast as a statistical inference problem and the Bayesian inversion is employed to reconstruct the coefficients of the eigen-expansion for the source function. The stability of the statistical inverse problem with respect to the measured data is justified in the sense of Hellinger distance. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings (MH) algorithm is implemented to explore the posterior density function. Numerical examples show that the proposed method is effective for both smooth and non-smooth sources.<br></p>