The First In Vitro and In Vivo Validation of the Hessian-Free Ray-Born Inversion for Quantitative Ultrasound Tomography

TL;DR

This paper validates a Hessian-free ray-Born inversion method for quantitative ultrasound tomography, demonstrating its accuracy and efficiency in reconstructing sound speed from ultrasound data in both in-vitro and in-vivo settings.

Contribution

First experimental validation of a Hessian-free ray-Born inversion technique for ultrasound tomography, combining high-frequency approximations with efficient Hessian inversion.

Findings

Accurately reconstructed sound speed images in vitro and in vivo.

Compared favorably with full-wave inversion results.

Demonstrated computational efficiency suitable for clinical use.

Abstract

This study presents the first experimental validation of a Hessian-free ray-Born inversion technique for quantitative reconstruction of sound speed from transmission ultrasound data. The method combines single-scattering theory with high-frequency approximations, yielding an inversion framework well suited to the frequency ranges used in clinical ultrasound applications. Unlike previous singly-scattered inversion approaches that account for medium heterogeneities only in the scattering potential, the proposed ray-Born method employs Green's functions approximated along ray trajectories determined by high-frequency assumptions. The associated objective function is linearized and minimized sequentially across increasing frequency bands. At each frequency set, the linearized subproblem is solved using a weighting scheme applied to both the solution and data spaces, which diagonalizes the Hessian and enables its inversion in a single step. The method, previously reported and released as an open-source package, was applied to in-vitro and in-vivo datasets provided by the University of Rochester Medical Center. The reconstructed images were evaluated by comparison with those obtained using a full-wave inversion approach based on a frequency-domain Helmholtz solver. The results demonstrate the strong potential of the Hessian-free ray-Born inversion as a computationally efficient and accurate method suitable for clinical translation.