Using optimal transport to mitigate cycle-skipping in ultrasound computed tomography

Full-waveform inversion (FWI) for ultrasound computed tomography is an advanced method to provide quantitative and high-resolution images of tissue properties. Two main reasons hindering the widespread adoption of FWI in clinical practice are (1) its high computational cost and (2) the requirement of a good initial model to mitigate the non-convexity of the inverse problem. The latter is commonly referred to as “cycle-skipping", which occurs for phase differences between synthetic and observed signals and usually traps the inversion in a local minimum. Source-encoding strategies, which simultaneously activate several emitters and have been proposed to reduce the simulation cost, further contribute to this issue due to the multiple arrivals of the wavefronts. We present a time-domain acoustic full-waveform inversion strategy utilizing a recently proposed misfit functional based on optimal transport. Using a graph-space formulation, the discrepancy between simulated and observed signals can be computed efficiently by solving an auxiliary linear program. This approach alleviates the common need for either a good initial model and / or low-frequency data. Furthermore, combining this misfit functional with random source-encoding and a stochastic trust-region method significantly reduces the computational cost per FWI iteration. In-silico examples using a numerical phantom for breast screening ultrasound tomography demonstrate the ability of the proposed inversion strategy to converge to the ground truth even when starting from a weak prior and cycle-skipped data.