Ultrasound imaging is a front-line clinical modality with a wide range of applications. However, there are limitations to conventional methods for some medical imaging problems, including the imaging of the intact brain. The goal of this thesis is to explore and build on recent technological advances in ultrasonics and related areas such as geophysics, including the ultrasound data parallel acquisition hardware, advanced computational techniques for field modelling and for inverse problem solving. With the significant increase in the computational power now available, a particular focus will be put on exploring the potential of full-waveform inversion (FWI), a high-resolution image reconstruction technique which has shown significant succes...