Full wave inversion uses all of the information from the wave and more intense computational tomography to image structures that pulse wave B mode cannot, though gases are still a problem. Computationally, if you squint, it's similar to the work Midjourney does with AI image generation, as it progressively generates a structure that fits the data.
Ultrasonic waves can penetrate most structures in humans, including the brain. For example, with focused ultrasound (as they mentioned with MRgFUS) you can burn specific structures in the middle of the brain without any incision.
To use this for imaging, you need lots of transducers (MRgFUS typically uses 1024 for ablation, and Midjourney is proposing 358,000 for imaging) and massive advances in computational tomography capabilities. There will still likely be pockets of low confidence where there's a lot of air, like in the lungs. But with sufficient information on what's happening around those areas, you'd still have something that's medically useful.
Ultrasound researcher here: this work is almost certainly not full wave inversion. You're right that FWI can be done in this kind of setup. Notably, a lot of people are trying to use circular arrays of ultrasound sensors to do FWI, particularly in the brain or the breast. But, it's a challenging inverse problem to solve and as far as I know, it's still extremely slow - nowhere near realtime.
The data they show is almost certainly a normal beamforming algorithm like delay and sum, possibly with some simple speed of sound correction. The most similar paper I know of is here in Nature Biomedical Engineering from a team at Caltech. https://www.nature.com/articles/s41551-026-01660-4