Misspecification of Multiple Scattering in Scalar Wave Fields and its Impact in Ultrasound Tomography

In this work, we investigate the localization of point-like targets in the presence of multiple scattering. We focus on the often omitted scenario in which measurement data is affected by multiple scattering, and a simpler model is employed in the estimation. We study the impact of such model mismatch by means of the Misspecified Cramér-Rao Bound (MCRB). In numerical simulations inspired by tomographic inspection in Ultrasound Nondestructive Testing (UNDT), the MCRB is shown to correctly describe the estimation variance of localization parameters under misspecification of the wave propagation model.We provide extensive discussion on the utility of the MCRB in the practical task of verifying whether a chosen misspecified model is suitable for localization based on the properties of the maximum likelihood estimator and the nuanced distinction between bias and parameter space differences. Finally, we highlight that careful interpretation is needed whenever employing the classical CRB in the presence of mismatch through numerical examples based on the Born approximation and other simplified propagation models stemming from it. Although motivated by UNDT, the analysis and discussion throughout this work generally apply to localization tasks based on scalar wave field measurements.