Bayesian Approach to Inverse Time-harmonic Acoustic Scattering from Sound-soft Obstacles with Phaseless Data

TL;DR

This paper presents a Bayesian framework for inverse acoustic scattering from sound-soft obstacles using phaseless data, employing advanced MCMC techniques and surrogate modeling to enhance efficiency and accuracy.

Contribution

It introduces a novel combination of Gibbs sampling, pCN algorithm, and gPC surrogate models to improve computational efficiency in high-dimensional inverse scattering problems.

Findings

Effective reduction in computational cost through surrogate modeling.

Successful application of Bayesian MCMC to phaseless inverse scattering.

Numerical results demonstrate improved convergence and accuracy.

Abstract

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 point source waves. To improve the convergence rate, we use the Gibbs sampling and preconditioned Crank-Nicolson (pCN) algorithm with random proposal variance to implement the Markov chain Monte Carlo (MCMC) method. This usually leads to heavy computational cost, since the unknown obstacle is parameterized in high dimensions. To overcome this challenge, we examine a surrogate model constructed by the generalized polynomial chaos (gPC) method to reduce the computational cost. Numerical examples are provided to illustrate the effectiveness of the proposed method.