# Limited Aperture Inverse Scattering Problems using Bayesian Approach and Extended Sampling Method

## TL;DR

This paper introduces a Bayesian approach combined with an extended sampling method to solve limited aperture inverse acoustic scattering problems, enabling obstacle shape reconstruction with proven well-posedness and efficient convergence.

## Contribution

It develops a novel Bayesian framework for limited aperture inverse scattering and modifies the extended sampling method for improved initial guesses, enhancing reconstruction accuracy.

## Key findings

- The method successfully reconstructs obstacle shapes from limited data.
- The Bayesian formulation is well-posed in the Hellinger metric.
- Numerical results demonstrate effective and fast convergence.

## Abstract

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is formulated as a statistical model using the Baye's formula. The well-posedness is proved in the sense of the Hellinger metric. The extended sampling method is modified to provide the initial guess of the target location, which is critical to the fast convergence of the MCMC algorithm. An extensive numerical study is presented to illustrate the performance of the proposed method.