Supervised Descent Method for Electrical Impedance Tomography

Abstract

Electrical impedance tomography (EIT) is a nonintrusive, radiation-free, and portable medical imaging modality. In this modality, an electrode array is arranged around a medical target to be imaged, and then currents are injected and the induced voltages are measured through the electrodes according to a certain protocol. The measured voltages can then be inverted to get an image that reflects the conductivity distribution interior of the medical target. The inverse problem of EIT can be formulated as a nonlinear optimization problem. It can be solved iteratively by using Gauss-Newton method, which is based on the quadratic approximation of the objective function locally.Supervised descent method (SDM) is a machine learning algorithm that is inspired by the Gauss-Newton method. It learns a series of descent directions which correspond to the product of the inverse Hessian and Jacobian through offline training. In the online inference stage, it uses the learned descent directions to invert the measured data. SDM has several advantages over the traditional Gauss-Newton method. Firstly, the time and memory cost is significantly reduced because there is no need to calculate the Jacobian and the inverse Hessian in the online inversion stage. Secondly, the a priori information can be integrated in a flexible manner through training samples. Thirdly, the learned descent directions have some global capability.In this work, we applied SDM to EIT data inversion. The training and inference problems were formulated. The algorithm was tested using both numerical and experimental examples. The results show SDM is feasible for EIT data inversion with good generalization ability.