Hessian-free Ray-Born Inversion for Quantitative Ultrasound Tomography of Weakly Heterogeneous Media

TL;DR

This paper introduces a computationally efficient Hessian-free ray-Born inversion method for quantitative ultrasound tomography, improving robustness to noise and enabling clinical application through innovative regularization and ray-tracing techniques.

Contribution

The study develops a Hessian-free inversion approach with a novel weighting scheme and paraxial ray-tracing, significantly reducing computational cost and enhancing robustness in ultrasound tomography.

Findings

Reduced computational expense by approximately an order of magnitude.

Achieved robust reconstructions less sensitive to noise.

Enabled clinical translation of acoustic inverse scattering methods.

Abstract

This study presents a frequency-domain, Hessian-free ray-Born inversion method for quantitative ultrasound tomography, extending the author's previous Hessian-based approach. Both approaches model acoustic wave propagation using a ray-based approximation of the Green's function in smoothly varying heterogeneous media, and perform the inversion iteratively in the frequency domain, progressing from low to high frequencies. In the earlier method, each frequency subproblem was solved through iterative inversion of the Hessian matrix, a process that not only increased computational cost but also made the update steps more sensitive to noise. The present work addresses these limitations by diagonalizing the Hessian matrix through a specific weighting scheme, which enables a single-step inversion for each frequency subproblem. This reformulation reduces the computational expense by approximately an order of magnitude relative to the Hessian-based approach. The weighting scheme also functions as a smoothing regularizer that is intrinsically embedded within the forward operator, thereby balancing computational efficiency and spatial resolution while producing robust reconstructions less sensitive to noise. Furthermore, for approximating the geometrical portion of the amplitude, this study introduces a paraxial ray-tracing system, further enhancing computational efficiency and accuracy. The inversion approach proposed in the present study has enabled the first successful translation of acoustic inverse scattering methods to a clinical setting.