Bayesian Approach to Inverse Time-harmonic Acoustic Scattering with Phaseless Far-field Data
Numerical Analysis
2021-07-28 v2 Numerical Analysis
Abstract
This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and kite-shaped obstacles through properly chosen incoming waves in two dimensions. Given the Gaussian prior measure, the well-posedness of the posterior measure in the Bayesian approach is discussed. The Markov Chain Monte Carlo (MCMC) method is adopted in the numerical approximation and the preconditioned Crank-Nicolson (pCN) algorithm with random proposal variance is utilized to improve the convergence rate. Numerical examples are provided to illustrate effectiveness of the proposed method.
Cite
@article{arxiv.1907.12431,
title = {Bayesian Approach to Inverse Time-harmonic Acoustic Scattering with Phaseless Far-field Data},
author = {Zhipeng Yang and Xinping Gui and Ju Ming and Guanghui Hu},
journal= {arXiv preprint arXiv:1907.12431},
year = {2021}
}