Neural network-based supervised descent method for 2D electrical impedance tomography

Abstract

Objective: In this work, we study the application of the neural network-based supervised descent method (NN-SDM) for 2D electrical impedance tomography. Approach: The NN-SDM contains two stages: offline training and online prediction. In the offline stage, neural networks are iteratively applied to learn a sequence of descent directions for minimizing the objective function, where the training data set is generated in advance according to prior information or historical data. In the online stage, the trained neural networks are directly used to predict the descent directions. Main results: Numerical and experimental results are reported to assess the efficiency and accuracy of the NN-SDM for both model-based and pixel-based inversions. In addition, the performance of the NN-SDM is compared with the linear SDM (LSDM), an end-to-end neural network (E2E-NN) and the Gauss-Newton (GN) method. The results demonstrate that the NN-SDM achieves faster convergence than the LSDM and GN method, and achieves a stronger generalization ability than the E2E-NN. Significance: The NN-SDM combines the strong non-linear fitting ability of the neural network and good generalization capability of the supervised descent method (SDM), which also provides good flexibility to incorporate prior information and accelerates the convergence of iteration.