# A Bayesian approach to improving the Born approximation for inverse scattering with high contrast materials

## TL;DR

This paper enhances the Born approximation in inverse scattering for high contrast materials by integrating Bayesian error modeling, allowing for improved reconstructions despite the approximation's limitations.

## Contribution

It introduces a Bayesian correction method to mitigate errors in the Born approximation for inverse scattering with high contrast media.

## Key findings

- Bayesian error modeling improves the accuracy of the Born approximation.
- The method extends the applicability of simplified models to high contrast scenarios.
- Numerical results demonstrate better reconstruction quality with the proposed approach.

## Abstract

Time harmonic inverse scattering using accurate forward models is often computationally expensive. On the other hand, the use of computationally efficient solvers, such as the Born approximation, may fail if the targets do not satisfy the assumptions of the simplified model. In the Bayesian framework for inverse problems, one can construct a statistical model for the errors that are induced when approximate solvers are used, and hence increase the domain of applicability of the approximate model. In this paper, we investigate the error structure that is induced by the Born approximation and show that the Bayesian approximation error approach can be used to partially recover from these errors. In particular, we study the model problem of reconstruction of the index of refraction of a penetrable medium from measurements of the far field pattern of the scattered wave.