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Bayesian approach to inverse time-harmonic acoustic obstacle scattering with phaseless data generated by point source waves. (English) Zbl 07427314

Summary: This paper concerns the Bayesian approach to inverse acoustic scattering problems of inferring the position and shape of a sound-soft obstacle from phaseless far-field data generated by two-dimensional point source waves. Given the total number of obstacle parameters, the Markov chain Monte Carlo (MCMC) method is employed to reconstruct the boundary of the obstacle in a high-dimensional space, which usually leads to slow convergence and prohibitively high computational cost. We use the Gibbs sampling and preconditioned Crank-Nicolson (pCN) algorithm with random proposal variance to improve the convergence rate, and design an effective strategy for the surrogate model constructed by the generalized polynomial chaos (gPC) method to reduce the computational cost of MCMC. Numerical examples are provided to illustrate the effectiveness of the proposed method.

MSC:

35R30 Inverse problems for PDEs
35P25 Scattering theory for PDEs
62F15 Bayesian inference
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
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