GraphEIT: Unsupervised Graph Neural Networks for Electrical Impedance Tomography

Convolutional Neural Networks (CNNs) based methodologies have found extensive application in Electrical Impedance Tomography (EIT). Convolution is commonly employed for uniform domains like pixel or voxel images. However, EIT reconstruction problem often involves nonuniform meshes, typically arising from finite element methods. Hence, reconciling nonuniform and uniform domains is essential. To address this issue, we propose an unsupervised reconstruction approach, termed GraphEIT, designed to tackle EIT problems directly on nonuniform mesh domains. The core concept revolves around representing conductivity via a fusion model that seamlessly integrates Graph Neural Networks (GNNs) and Multi-layer Perceptron networks (MLPs). Operating in an unsupervised manner eliminates the requirement for labeled data. Additionally, we incorporate Fourier feature projection to counter neural network spectral bias, thereby guiding the network to capture high-frequency details. Comprehensive experiments demonstrate the effectiveness of our proposed method, showcasing notable improvements in sharpness and shape preservation. Comparative analyses against state-of-the-art techniques underscore its superior convergence capability and robustness, particularly in the presence of measurement noise.