Imaging Conductivity from Current Density Magnitude using Neural Networks

TL;DR

This paper introduces a neural network method for reconstructing tissue conductivity from current density magnitude, formulated as a relaxed optimization problem, demonstrating robustness to noise in numerical experiments.

Contribution

It develops a novel neural network approach for conductivity imaging from current density magnitude, with theoretical error bounds and empirical validation.

Findings

Robustness to data noise demonstrated in experiments

Explicit bounds on approximation and statistical errors derived

Effective reconstruction of conductivity in numerical tests

Abstract

Conductivity imaging represents one of the most important tasks in medical imaging. In this work we develop a neural network based reconstruction technique for imaging the conductivity from the magnitude of the internal current density. It is achieved by formulating the problem as a relaxed weighted least-gradient problem, and then approximating its minimizer by standard fully connected feedforward neural networks. We derive bounds on two components of the generalization error, i.e., approximation error and statistical error, explicitly in terms of properties of the neural networks (e.g., depth, total number of parameters, and the bound of the network parameters). We illustrate the performance and distinct features of the approach on several numerical experiments. Numerically, it is observed that the approach enjoys remarkable robustness with respect to the presence of data noise.