A Two-Step Inverse Algorithm for Biomedical Magnetic Induction Tomography With Neural Networks: Introduction and Error Analysis

Abstract

Medical imaging is a continuously evolving field with a constant need for advancements in its capabilities and applications. Magnetic induction tomography (MIT) represents a promising alternative to the established imaging methods. MIT is a non-invasive and cost-effective tomography method with considerable potential for biomedical imaging. Nevertheless, the inverse problem associated with MIT is inherently difficult to resolve using conventional techniques, primarily due to its ill-conditioned and nonlinear nature. The application of machine learning methods offers an elegant solution to the image reconstruction process. In contrast with the conventional approach of directly reconstructing images from measured signals, the inverse algorithm proposed here is divided into two subproblems. This approach was inspired by the physics of the forward problem. Specifically, the underlying currents are first reconstructed from the signals and then the conductivity distribution is reconstructed from those in the second step. For each of those problems, specifically designed neural networks were employed. This approach demonstrated very good reconstruction quality, as evidenced by excellent metrics on the test dataset, which differed significantly from the training data. Furthermore, an extensive error analysis was conducted to identify the strengths and weaknesses of the image reconstruction process.

Keywords

• Deep learning
• image reconstruction
• inverse problems
• magnetic induction tomography