# Bayesian Approach to Inverse Time-harmonic Acoustic Scattering with Phaseless Far-field Data

## TL;DR

This paper introduces a Bayesian method for reconstructing sound-soft obstacles from phaseless far-field data in inverse acoustic scattering, utilizing MCMC techniques for improved numerical approximation.

## Contribution

It develops a Bayesian framework for inverse scattering with phaseless data and demonstrates the effectiveness of pCN-MCMC algorithms for obstacle reconstruction.

## Key findings

- Successful reconstruction of various obstacle shapes
- Effective use of pCN-MCMC for convergence
- Validation through numerical examples

## 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.