# Bayesian approach for inverse obstacle scattering with Poisson data

## TL;DR

This paper develops a Bayesian inversion method for reconstructing acoustic obstacles from Poisson data, incorporating hybrid priors including Gaussian and total variation to improve the reconstruction quality.

## Contribution

It introduces a Bayesian framework with hybrid priors for inverse obstacle scattering with Poisson data, and discusses the well-posedness of the posterior distribution.

## Key findings

- Numerical examples demonstrate the effectiveness of the proposed algorithm.
- Hybrid priors improve reconstruction accuracy.
- The approach handles stochastic Poisson data effectively.

## Abstract

We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form. The prior for the parameterized unknown plays key role in the Bayes reconstruction algorithm. The most popular used prior is the Gaussian. Under the Gaussian prior assumption, we further suppose that the unknown satisfies the total variation prior. With the hybrid prior, the well-posedness of the posterior distribution is discussed. The numerical examples verify the effectiveness of the proposed algorithm.