A Bayesian level set method for inverse source scattering problems with multi-frequencies

Abstract

This paper concerns the reconstruction of the support of source function based on the Bayesian level set approach. The unknown source to be reconstructed is assumed to be piecewise constant with a known value. In this setting, the support of the source function can be characterized by the level set functions. In the Bayesian level set inversion, the solution of the inverse problem is posterior distribution. The Markov Chain Monte Carlo (MCMC) algorithm is applied to generate the samples of the posterior distribution. The numerical results show the effectiveness of the proposed method and the dependence of the posterior samples on the flexible and proper smoothness priors with the Whittle-Matérn Gaussian random fields.