Quality-Bayesian Approach to Inverse Acoustic Source Problems with Partial Data

Abstract

A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling method by constructing new indicator functions to obtain the approximate locations of the sources. The behavior of the indicators is analyzed. Second, the inverse problem is formulated as a statistical inference problem using the Bayes' formula. The well-posedness of the posterior distribution is proved. The source locations obtained in the first step are coded in the priors. Then a Metropolis--Hastings Markov chain Monte Carlo algorithm is used to explore the posterior density. Both steps use the same physical model and measured data. Numerical experiments show that the proposed method using partial data is effective.