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We propose a deterministic-statistical method for an inverse source problemusing multiple frequency limited aperture far field data. The direct samplingmethod is used to obtain a disc such that it contains the compact support ofthe source. The Dirichlet eigenfunctions of the disc are used to expand thesource function. Then the inverse problem is recast as a statistical inferenceproblem for the expansion coefficients and the Bayesian inversion is employedto reconstruct the coefficients. The stability of the statistical inverseproblem with respect to the measured data is justified in the sense ofHellinger distance. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings(MH) algorithm is implemented to explore the posterior density function of theunknowns. Numerical examples show that the proposed method is effective forboth smooth and non-smooth sources given limited-aperture data.

Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data