A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound
A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound
复制标题
DOI：
10.1016/j.jcp.2021.110430
复制
发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
A. Stanziola;S. Arridge;B. Cox;B. Treeby
中科院分区：
文献类型：
--
作者：
A. Stanziola;S. Arridge;B. Cox;B. Treeby
经颅超声治疗被越来越多地用于脑部疾病的非侵入性治疗。然而，传统的数值波解算器目前计算成本太高，不能在治疗期间在线使用，以预测穿过头骨的声场(例如，为了考虑特定受试者的剂量和靶向变化)。作为迈向实时预测的一步，在当前的工作中，使用完全学习的优化器开发了二维非均匀Helmholtz方程的快速迭代求解器。该轻量级网络体系结构基于包括学习的隐藏状态的修改的NET。使用基于物理的损失函数和一组理想化的声速分布以及完全无监督的训练来训练网络(不需要知道真正的解决方案)。所学习的优化器在测试集上表现出出色的性能，并且能够很好地泛化到训练样本之外，包括更大的计算域，以及更复杂的源和声速分布，例如来自头骨的X射线计算机断层成像图像的源和声速分布。
Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict the acoustic field passing through the skull (e.g., to account for subject-specific dose and targeting variations). As a step towards real-time predictions, in the current work, a fast iterative solver for the heterogeneous Helmholtz equation in 2D is developed using a fully-learned optimizer. The lightweight network architecture is based on a modified UNet that includes a learned hidden state. The network is trained using a physics-based loss function and a set of idealized sound speed distributions with fully unsupervised training (no knowledge of the true solution is required). The learned optimizer shows excellent performance on the test set, and is capable of generalization well outside the training examples, including to much larger computational domains, and more complex source and sound speed distributions, for example, those derived from x-ray computed tomography images of the skull.