Open-source Gauss-Newton-based methods for refraction-corrected ultrasound computed tomography

This work presents refraction-corrected sound speed reconstruction techniques for transmission-based ultrasound computed tomography using a circular transducer array. Pulse travel times between element pairs can be calculated from slowness (the reciprocal of sound speed) using the eikonal equation. Slowness reconstruction is posed as a nonlinear least squares problem where the objective is to minimize the error between measured and forward-modeled pulse travel times. The Gauss-Newton method is used to convert this problem into a sequence of linear least-squares problems, each of which can be efficiently solved using conjugate gradients. However, the sparsity of ray-pixel intersection leads to ill-conditioned linear systems and hinders stable convergence of the reconstruction. This work considers three approaches for resolving the ill-conditioning in this sequence of linear inverse problems: 1) Laplacian regularization, 2) Bayesian formulation, and 3) resolution-filling gradients. The goal of this work is to provide an open-source example and implementation of the algorithms used to perform sound speed reconstruction, which is currently being maintained on Github: https://github.com/ rehmanali1994/refractionCorrectedUSCT.github.io.