Impact of the Born approximation on the estimation error in 2D inverse scattering

The aim is to quantify the impact of the Born approximation on the estimation error for a simple inverse scattering problem, while taking into account the noise measurement features. The proposed method consists of comparing two estimation errors: the error obtained with the Born approximation and the error obtained without it. The first error is characterized by the mean and variance of the maximum likelihood estimator, which are straightforward to compute with the Born approximation because the corresponding estimator is linear. The second error is evaluated with the Cramer–Rao bound (CRB). The CRB is a lower bound on the variance of unbiased estimators and thus does not depend on the choice of the estimation method. Beyond the conclusions that will be established under the Born approximation, this study lays out a general methodology that can be generalized to any other approximation. (paper)