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

TL;DR

This paper examines how ignoring multiple scattering in ultrasound tomography affects target localization accuracy, using the Misspecified Cramér-Rao Bound to analyze the impact of model mismatch.

Contribution

It introduces the use of the MCRB to evaluate localization variance under model misspecification in ultrasound tomography, providing practical insights for model validation.

Findings

MCRB accurately predicts estimation variance with model mismatch

Classical CRB can be misleading under model misspecification

Careful interpretation of bounds is essential in practical scenarios

Abstract

In this work, we investigate the localization of 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 Cram\'er-Rao Bound (MCRB). In numerical simulations inspired by tomographic inspection in ultrasound nondestructive testing, 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.