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 introduce a novel 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.

中文翻译：

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时域全波形反演的高分辨率3D超声乳腺成像

超声波断层扫描（UST）扫描仪可以导出人体乳房声学特性的定量图像，并在筛查，诊断和治疗计划中具有潜在的应用前景。时域全波形反演（TD-FWI）是一种很有前途的UST图像形成技术，通过基于梯度的优化来拟合波物理模型的参数场。对于高分辨率3D UST，它面临三个主要挑战：首先，其中心构件（用于单个US测量的梯度计算）具有有限的大内存占用。其次，需要为$ 10 ^ 3-10 ^ 4 $的每个测量值计算此构造块，从而导致通常在大型计算集群上执行大量并行计算达数天。最后，基础优化问题的结构可能会导致求解器的进度缓慢并收敛到局部最小值。在这项工作中，我们设计和评估了克服这些挑战的综合计算策略：首先，我们引入了一种基于时间反转的新颖梯度计算，该梯度计算显着减少了内存占用，但每个源额外增加了一次波形仿真。其次，我们通过使用源编码（SE）计算随机梯度估计来打破对测量次数的依赖。我们还描述了一种具有更精确的方差控制的更准确的TD特定SE技术，并使用了最新的随机LBFGS方法。最后，我们设计了一种有效的TD多网格方案，并进行了预处理，以加快收敛速度​​，同时避免出现局部极小值。所有组件均通过模拟碗形3D UST乳房扫描仪原型的大量数字概念验证研究进行评估。最后，我们证明了它们的组合使我们能够在24h内使用Matlab在单个GPU上以0.5mm的分辨率获得准确的442x442x222体素图像。