论文标题
使用神经网络来自电流密度幅度的成像电导率
Imaging Conductivity from Current Density Magnitude using Neural Networks
论文作者
论文摘要
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，用于从内部电流密度的幅度成像电导率。它是通过将问题提出为放松的加权最小梯度问题，然后通过标准完全连接的前馈神经网络近似其最小化器来实现的。我们在概括误差的两个组成部分（即近似误差和统计误差）上得出界限，这是根据神经网络的属性（例如，深度，参数总数以及网络参数的界限）明确的。我们说明了几个数值实验中该方法的性能和不同特征。从数值上讲，观察到该方法相对于数据噪声的存在具有显着的鲁棒性。
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.
