The First In Vitro and In Vivo Validation of the Hessian-Free Ray-Born Inversion for Quantitative Ultrasound Tomography
Ashkan Javaherian
TL;DR
This work validates a Hessian-free ray-Born inversion for quantitative ultrasound tomography, enabling stable, single-step Hessian inversion updates $\delta c$ across increasing frequencies to reconstruct sound-speed maps from transmission data. By modeling the forward problem with ray-based Green's functions and incorporating singly scattered waves, the method achieves low-artifact, quantitatively accurate reconstructions that compare favorably with full-wave Helmholtz inversions while offering computational efficiency. The approach is implemented in open-source MATLAB tools and demonstrated on URMC in vitro phantoms and in vivo breast data, highlighting its potential for clinical translation and integration with hybrid imaging workflows. While performance is currently bounded by MATLAB, the framework provides a scalable platform for future compiled implementations and finer-reconstruction grids.
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.