GaBUS: Gaussian Beam framework for Ultrasound Computed Tomography

Abstract: In this project we propose a new framework for performing ultrasound tomography (UST) reconstruction based on Gaussian Beams (GBs). GBs are generalisations of ray solutions with complex phase and amplitude functions defined everywhere even on the caustics. The complexity of a propagation of a single GB on an Nd cube grid is O(N). Naively representing each of O(Nd-1) omnidirectional sources as O(Nd-1) directional GBs would already result in a reduced complexity O(N2d-1) for the forward operator. We can achieve further improvements by fully exploiting the rich GB parametrisation and their relationship with the wave atoms.