for: This study aims to investigate the potential of deep generative models (DGMs) in learning implicit regularizers for Electrical Impedance Tomography (EIT) imaging.
methods: The study uses three DGMs - variational autoencoder networks, normalizing flow, and score-based diffusion model - to learn implicit regularizers for EIT inverse problems.
results: The study shows that no single method consistently outperforms the others across all settings, and the conditional normalizing flow model (CNF) exhibits the best generalization in low-level noise, while the conditional score-based diffusion model (CSD*) demonstrates the best generalization in high-level noise settings.Abstract
Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present challenges for classical regularization techniques, such as the critical selection of regularization terms and the lack of prior knowledge. Deep generative models (DGMs) have been shown to play a crucial role in learning implicit regularizers and prior knowledge. This study aims to investigate the potential of three DGMs-variational autoencoder networks, normalizing flow, and score-based diffusion model-to learn implicit regularizers in learning-based EIT imaging. We first introduce background information on EIT imaging and its inverse problem formulation. Next, we propose three algorithms for performing EIT inverse problems based on corresponding DGMs. Finally, we present numerical and visual experiments, which reveal that (1) no single method consistently outperforms the others across all settings, and (2) when reconstructing an object with 2 anomalies using a well-trained model based on a training dataset containing 4 anomalies, the conditional normalizing flow model (CNF) exhibits the best generalization in low-level noise, while the conditional score-based diffusion model (CSD*) demonstrates the best generalization in high-level noise settings. We hope our preliminary efforts will encourage other researchers to assess their DGMs in EIT and other nonlinear inverse problems.
摘要
电气阻抗成像（EIT）是广泛应用的成像技术在工业检查、地球物理探测和医疗成像中。然而，EIT图像重建中的内在非线性和不稳定性使得经典正则化技术难以应用。深度生成模型（DGM）已经被证明可以扮演重要的隐式正则化和先知知识角色。本研究旨在调查DGM在学习基于EIT成像的情况下是否能够学习隐式正则化。我们首先介绍EIT成像和其反向问题的背景信息。然后，我们提出了基于不同DGM的三种算法来解决EIT反向问题。最后，我们通过数值和视觉实验发现，(1) 不同的方法在不同的设定下并不一定能够优于其他方法，(2) 使用训练集中包含4个畸形的模型来重建含2个畸形的物体时，在低噪声设定下， conditional normalizing flow模型（CNF）表现最佳，而在高噪声设定下， conditional score-based diffusion模型（CSD*) 表现最佳。我们希望我们的初步努力能够激励其他研究人员通过自己的DGM来探索EIT和其他非线性反向问题。