  Ultrasound tomography (UST) scanners allow quantitative images of the human
breast's acoustic properties to be derived with potential applications in
screening, diagnosis and therapy planning. Time domain full waveform inversion
(TD-FWI) is a promising UST image formation technique that fits the parameter
fields of a wave physics model by gradient-based optimization. For high
resolution 3D UST, it holds three key challenges: Firstly, its central building
block, the computation of the gradient for a single US measurement, has a
restrictively large memory footprint. Secondly, this building block needs to be
computed for each of the $10^3-10^4$ measurements, resulting in a massive
parallel computation usually performed on large computational clusters for
days. Lastly, the structure of the underlying optimization problem may result
in slow progression of the solver and convergence to a local minimum. In this
work, we design and evaluate a comprehensive computational strategy to overcome
these challenges: Firstly, we exploit a gradient computation based on time
reversal that dramatically reduces the memory footprint at the expense of one
additional wave simulation per source. Secondly, we break the dependence on the
number of measurements by using source encoding (SE) to compute stochastic
gradient estimates. Also we describe a more accurate, TD-specific SE technique
with a finer variance control and use a state-of-the-art stochastic LBFGS
method. Lastly, we design an efficient TD multi-grid scheme together with
preconditioning to speed up the convergence while avoiding local minima. All
components are evaluated in extensive numerical proof-of-concept studies
simulating a bowl-shaped 3D UST breast scanner prototype. Finally, we
demonstrate that their combination allows us to obtain an accurate 442x442x222
voxel image with a resolution of 0.5mm using Matlab on a single GPU within 24h.
