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.

翻译：电阻抗层析成像（EIT）广泛应用于医学诊断、工业检测和环境监测。结合成像系统的物理原理与数据驱动深度学习网络的优势，物理嵌入型深度展开网络近年来已成为计算成像领域极具前景的解决方案。然而，EIT图像重建固有的非线性与病态特性，仍对现有方法的精度与稳定性构成挑战。为解决这一难题，我们提出学习型半二次分裂（HQSNet）算法，将物理机制融入基于学习的EIT成像。随后，我们将安德森加速（AA）应用于HQSNet算法，记为AA-HQSNet，该算法可分别视为AA应用于HQSNet的高斯-牛顿步与学习型近端梯度下降步。AA是一种广泛用于加速不动点迭代算法收敛的技术，在数值优化与机器学习领域备受关注。然而，该技术在逆问题领域至今鲜受关注。与标准HQSNet相比，应用AA提升了收敛速率，同时避免了重建伪影。最后，我们通过严格的数值与视觉实验证明，AA模块强化了HQSNet，使其相比现有最优方法实现了鲁棒、精确且显著更优的重建效果。我们提出的增强HQSNet的安德森加速方案具有通用性，可用于提升各类物理嵌入型深度学习方法的性能。