Clinical diagnosis and treatment of stroke is limited by the absence of rapid, transportable, cost-effective and universally safe brain imaging. Full-waveform inversion (FWI) of transcranial ultrasound has recently been proposed as a potential solution.

Despite its promise, a fundamental limitation of FWI is that it is a highly non-linear inverse problem. I address this through the transfer of various geophysical imaging techniques to medical ultrasound. Superior performance across numerous tests is obtained by graph-space optimal transport and adaptive waveform inversion.

I then explore the clinical utility of FWI for stroke diagnosis by constructing an anatomically realistic data set of acoustic properties for stroke-perturbed human head models, for which three-dimensional in silico experiments were conducted. The results demonstrate that FWI is able to illuminate all stroke-relevant features that are currently detectable using diagnostic stroke-related clinical neuroimaging techniques.

Commonalities between FWI and machine learning have been exploited throughout this thesis via the creation and use of a PyTorch-based FWI library. This facilitated the regularisation of FWI using traditional priors, and the development of a deep learning-based prior that leverages the hierarchical nature of pre-trained convolutional neural networks. Finally, I introduce the Wiener diffusion, a novel non-parametric generative model. I demonstrate that it is well suited to tasks with limited data, is flexible at inference time, and discuss how it can be readily incorporated within FWI to improve and accelerate convergence.

The findings of this research have the potential to significantly enhance the utility of brain imaging, particularly in the diagnosis of stroke, a major contributor to global mortality and impairment.