Incorporating Gauss-Newton Anderson Acceleration into Deep Learning with Applications to EIT Inverse Problems

Numerical methods like Gauss-Newton algorithm have a long-standing history in successfully solving nonlinear ill-posed problems, with applications ranging from phase retrieval to PDE-based Electrical Impedance Tomography (EIT). However, the convergence rate of the traditional numerical methods can be slow, especially for ill-conditioned

problems. To improve its convergence rate, in this research, we introduce an accelerated scheme for numerical methods based on Anderson acceleration and prove its convergence under reasonable conditions. We further propose a

learning-based framework that uses learned deep neural network to model the accelerated numerical methods, motivated by the fact that physics-embedded deep learning has emerged as the predominant approach in the scientific computing field such as computational imaging problems. Then, numerical experiments of EIT reconstruction can

be conducted to verify that the proposed approach can improve the convergence rate as well as obtain superior reconstructions compared to state-of-the-art methods.