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Enhancing Electrical Impedance Tomography Reconstruction Using Learned Half-Quadratic Splitting Networks with Anderson Acceleration

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Abstract

Electrical Impedance Tomography (EIT) is widely applied in medical diagnosis, industrial inspection, and environmental monitoring. Combining the physical principles of the imaging system with the advantages of data-driven deep learning networks, physics-embedded deep unrolling networks have recently emerged as a promising solution in computational imaging. However, the inherent nonlinear and ill-posed properties of EIT image reconstruction still present challenges to existing methods in terms of accuracy and stability. To tackle this challenge, we propose the learned half-quadratic splitting (HQSNet) algorithm for incorporating physics into learning-based EIT imaging. We then apply Anderson acceleration (AA) to the HQSNet algorithm, denoted as AA-HQSNet, which can be interpreted as AA applied to the Gauss-Newton step and the learned proximal gradient descent step of the HQSNet, respectively. AA is a widely-used technique for accelerating the convergence of fixed-point iterative algorithms and has gained significant interest in numerical optimization and machine learning. However, the technique has received little attention in the inverse problems community thus far. Employing AA enhances the convergence rate compared to the standard HQSNet while simultaneously avoiding artifacts in the reconstructions. Lastly, we conduct rigorous numerical and visual experiments to show that the AA module strengthens the HQSNet, leading to robust, accurate, and considerably superior reconstructions compared to state-of-the-art methods. Our Anderson acceleration scheme to enhance HQSNet is generic and can be applied to improve the performance of various physics-embedded deep learning methods.

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Data Availability

The datasets generated during and/or analysed during the current study are available in the https://github.com/CCcodecod/AA-HQSNet.

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Acknowledgements

The work is supported by the NSF of China (12101614) and the NSF of Hunan (2021JJ40715). We are grateful to the High Performance Computing Center of Central South University for assistance with the computations.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

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  1. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, China

    Guixian Xu, Huihui Wang & Qingping Zhou

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  1. Guixian Xu
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Correspondence to Qingping Zhou.

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Xu, G., Wang, H. & Zhou, Q. Enhancing Electrical Impedance Tomography Reconstruction Using Learned Half-Quadratic Splitting Networks with Anderson Acceleration. J Sci Comput 98, 49 (2024). https://doi.org/10.1007/s10915-023-02439-4

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