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 two anomalies using a well-trained model based on a training dataset containing four anomalies, the conditional normalizing flow (CNF) model 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.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 12101614
Funding source: Natural Science Foundation of Hunan Province
Award Identifier / Grant number: 2021JJ40715
Funding statement: The work is supported by the NSF of China (12101614) and the NSF of Hunan (2021JJ40715).
Acknowledgements
We are grateful to the High-Performance Computing Center of Central South University for assistance with the computations.
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