Physics Department, Faculty of Science, Sohag University, Egypt.
Institute for Multiscale Simulation, Department of Chemical and Biological Engineering, Friedrich-Alexander University of Erlangen-Nürnberg, Cauerstrae 3, D-91058 Erlangen, Germany.
Physiol Meas. 2024 Apr 18;45(4). doi: 10.1088/1361-6579/ad39c2.
The objective of this study was to propose a novel data-driven method for solving ill-posed inverse problems, particularly in certain conditions such as time-difference electrical impedance tomography for detecting the location and size of bubbles inside a pipe.We introduced a new layer architecture composed of three paths: spatial, spectral, and truncated spectral paths. The spatial path processes information locally, whereas the spectral and truncated spectral paths provide the network with a global receptive field. This unique architecture helps eliminate the ill-posedness and nonlinearity inherent in the inverse problem. The three paths were designed to be interconnected, allowing for an exchange of information on different receptive fields with varied learning abilities. Our network has a bottleneck architecture that enables it to recover signal information from noisy redundant measurements. We named our proposed model truncated spatial-spectral convolutional neural network (TSS-ConvNet).Our model demonstrated superior accuracy with relatively high resolution on both simulation and experimental data. This indicates that our approach offers significant potential for addressing ill-posed inverse problems in complex conditions effectively and accurately.The TSS-ConvNet overcomes the receptive field limitation found in most existing models that only utilize local information in Euclidean space. We trained the network on a large dataset covering various configurations with random parameters to ensure generalization over the training samples.
本研究旨在提出一种新颖的数据驱动方法来解决不适定反问题，特别是在某些条件下，如用于检测管道内气泡位置和大小的时差分电阻抗断层成像。我们引入了一种由三条路径组成的新的层架构：空间路径、频谱路径和截断频谱路径。空间路径局部处理信息，而频谱路径和截断频谱路径为网络提供全局感受野。这种独特的架构有助于消除反问题中的不适定性和非线性。三条路径被设计为相互连接，允许在不同的感受野上进行信息交换，同时具有不同的学习能力。我们的网络具有瓶颈架构，使其能够从噪声冗余测量中恢复信号信息。我们将提出的模型命名为截断空间-频谱卷积神经网络（TSS-ConvNet）。我们的模型在模拟和实验数据上都表现出了较高的准确性和相对较高的分辨率，这表明我们的方法在复杂条件下有效地解决不适定反问题具有很大的潜力。TSS-ConvNet 克服了大多数现有模型存在的感受野限制，这些模型仅在欧几里得空间中利用局部信息。我们在一个包含各种随机参数配置的大数据集上训练网络，以确保对训练样本的泛化能力。
