Hessian-free Ray-Born Inversion for Quantitative Ultrasound Tomography

Abstract: This study introduces a frequency-domain, Hessian-free ray-Born inversion method for quantitative ultrasound tomography, building upon the Hessian-based approach presented in our previous work. Both methods model acoustic wave propagation using a ray-based approximation of the heterogeneous Green's function and iteratively solve the inverse problem in the frequency domain, progressing from low to high frequencies. In the previous study, each frequency subproblem is solved by iterative inversion of the Hessian matrix, which significantly increases computational costs. The present study addresses this limitation by diagonalizing the Hessian matrix through specific weighting, enabling a single-step inversion for each subproblem. This modification reduces computational expense by approximately an order of magnitude compared to the Hessian-based method, bringing its efficiency in line with radon-type, time-of-flight-based methods that use bent rays. Furthermore, by incorporating regularization directly into the forward operator and balancing computational efficiency with spatial resolution, the Hessian-free method achieves robust image reconstructions that are less sensitive to noise and inaccuracies in the initial model. For the ray-based approximation, this study introduces a paraxial ray-tracing system. Instead of independently tracing an auxiliary ray, the Jacobian of the ray is approximated by simultaneously tracing a paraxial ray alongside the linked ray. This approach improves computational efficiency while maintaining accuracy.