Hessian-inversion-free ray-born inversion for quantitative ultrasound tomography

This study proposes a Hessian-inversion-free ray-born inversion approach for biomedical ultrasound tomography. The proposed approach is a more efficient version of the ray-born inversion approach proposed in [3]. Using these approaches, the propagation of acoustic waves are modelled using a ray approximation to heterogeneous Green's function. The inverse problem is solved in the frequency domain by iteratively linearisation and minimisation of the objective function from low to high frequencies. In [3], the linear subproblem associated with each frequency interval is solved by an implicit and iterative inversion of the Hessian matrix (inner iterations). Instead, this study applies a preconditioning approach on each linear subproblem so that the Hessian matrix becomes diagonalised, and can thus be inverted in a single step. Using the proposed preconditioning approach, the computational cost of solving each linear subproblem of the proposed ray-Born inversion approach becomes almost the same as solving one linear subproblem associated with a radon-type time-of-flight-based approach using bent rays. More importantly, the smoothness assumptions made for diagonalising the Hessian matrix make the image reconstruction more stable than the inversion approach in [3] to noise.