基于神经网络的电导率电流密度成像
Imaging Conductivity from Current Density Magnitude using Neural Networks
摘要：
电导率成像是医学成像中最重要的任务之一。在这项工作中，我们开发了一种基于神经网络的重建技术，从内部电流密度的大小成像的电导率。它是通过制定一个放松的加权最小梯度问题的问题，然后近似的标准全连接前馈神经网络的最小值。我们推导出泛化误差的两个分量的界，即，近似误差和统计误差，明确地根据神经网络的属性（例如，深度、参数总数和网络参数的边界）。我们说明了几个数值实验的方法的性能和独特的功能。数值上，它是观察到的方法享有显着的鲁棒性相对于数据噪声的存在。
英文摘要：
Conductivity imaging represents one of the most important tasks in medical imaging. In this work we develop a neural network based reconstruction technique for imaging the conductivity from the magnitude of the internal current density. It is achieved by formulating the problem as a relaxed weighted least-gradient problem, and then approximating its minimizer by standard fully connected feedforward neural networks. We derive bounds on two components of the generalization error, i.e., approximation error and statistical error, explicitly in terms of properties of the neural networks (e.g., depth, total number of parameters, and the bound of the network parameters). We illustrate the performance and distinct features of the approach on several numerical experiments. Numerically, it is observed that the approach enjoys remarkable robustness with respect to the presence of data noise.
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