Solving electrical impedance tomography with deep learning

Abstract

This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on the albedo operator that is accessible from boundary measurements. Both the forward map from the optical properties to the albedo operator and the inverse map are high-dimensional and nonlinear. For the circular tomography geometry, a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular direction. Motivated by this, we propose effective neural network architectures for the forward and inverse maps based on convolution layers, with weights learned from training datasets. Numerical results demonstrate the efficiency of the proposed neural networks.

Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks

“…Based on H-matrix and H 2 -matrix structure, Fan and his coauthors proposed two multiscale neural networks [20,21], which are more suitable in training smooth linear or nonlinear operators due to the multiscale nature of H-matrices. In addition to that, nonstandard wavelet form inspired the design of BCR-Net [22], which is applied to address the inverse of elliptic operator and nonlinear homogenization problem and recently been embedded in a neural network for solving electrical impedance tomography [19] and pseudo-differential operator [23]. Multigrid method also inspired MgNet [25].…”

A Review of Algorithms and Hardware Implementations in Electrical Impedance Tomography (Invited)

“…With the development of both algorithms and hardware implementations, intensive progresses have been achieved in EIT technique. For example, the learning algorithm becomes more and more attractive in the inverse problem, where stunning success has been shown in reconstructed image quality, robustness, and speed of solving EIT problems [20,36,[41][42][43][44][45][46]. In this section, we will review and classify some classical reconstruction algorithms and discuss possible improved methods.…”

“…Although DNN can potentially be used to approximate the inverse mapping F −1 due to its elasticity in representing high nonlinear functions as well as a data-driven regularization prior taken out automatically from the data [41], the direct learning approach actually works weakly if the input of the NN is set to the measured value, and the output is the value to be reconstructed as shown in Eq. (10).…”

Efficient Image Reconstruction Algorithm for ECT System Using Local Ensemble Transform Kalman Filter

“…This research will focus on electrical tomography methods [13], [14]. The electrical tomography systems, such as the Electrical Resistivity Tomography (ERT) [15], [16], Magnetic Induction Tomography (MIT) [17]- [19], and Electrical Capacitance Tomography (ECT) [20]- [24] are interesting. These modalities are real-time imaging, safe, suitable for different vessel sizes, and inexpensive.…”