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.

本研究提出了一种基于物理学知识的深度学习算法，将 Anderson 加速方法应用于 Half-Quadratic Splitting 网络中，以提高电阻抗成像的精度和稳定性。实验表明，这种算法在重建图像的同时，能够避免伪影和噪点的产生，具有一定的优势。