Landweber Iterative Image Reconstruction Method Incorporated Deep Learning for Electrical Resistance Tomography

Abstract

Electrical resistance tomography (ERT) is an efficient technology for rapid, accurate, and real-time monitoring of the dynamic of industrial process. However, due to the inherent nonlinearity and ill-posed, image reconstruction of ERT remains a challenging problem of significant importance for industrial visualization. A novel Landweber iterative reconstruction network (LIRN) that combines the mathematical structure of Landweber iterative reconstruction method with deep learning is proposed. As an iterative algorithm, the proposed method solves the problem of parameters selection, and as a deep learning method, LIRN has less dependence on incomplete databases and better generalization capabilities compared with the black box models. Each layer of the LIRN is composed of three parts: fully connected subnet, convolution subnet, and the output of the former layer. The output of the former layer is mapped to the outputs of the two subnets, which constitutes the residual module. The fully connected subnet is used to represent the gradient of the data fidelity, in which the relaxation factor vector is a learnable parameter corresponding to the weights of the subnet. The convolution subnet as a self-learning regularizer learns the image prior information. During the training process of LIRN, the relaxation factor vector and the image prior information are jointly trained and learned. The experimental and analytical results demonstrate that the proposed image reconstruction network with four layers can achieve a better reconstruction distribution than the traditional imaging methods and the existing image reconstruction algorithms based on deep learning.