Beltrami-Net: Domain Independent Deep D-bar Learning for Absolute Imaging with Electrical Impedance Tomography (a-EIT)

TL;DR

This paper introduces Beltrami-Net, a boundary shape independent deep learning approach combined with D-bar methods for real-time absolute EIT imaging, improving image quality and robustness.

Contribution

It presents a novel boundary shape independent training method for deep learning in EIT, enabling more generalizable and robust image reconstruction.

Findings

Significant image quality improvements with CNN post-processing.

Boundary shape independence allows training without specific domain knowledge.

Effective on experimental data from multiple EIT systems.

Abstract

Objective: To develop, and demonstrate the feasibility of, a novel image reconstruction method for absolute Electrical Impedance Tomography (a-EIT) that pairs deep learning techniques with real-time robust D-bar methods. Approach: A D-bar method is paired with a trained Convolutional Neural Network (CNN) as a post-processing step. Training data is simulated for the network using no knowledge of the boundary shape by using an associated nonphysical Beltrami equation rather than simulating the traditional current and voltage data specific to a given domain. This allows the training data to be boundary shape independent. The method is tested on experimental data from two EIT systems (ACT4 and KIT4). Main Results: Post processing the D-bar images with a CNN produces significant improvements in image quality measured by Structural SIMilarity indices (SSIMs) as well as relative $\ell_2$ and $\ell_1$ image errors. Significance: This work demonstrates that more general networks can be trained without being specific about boundary shape, a key challenge in EIT image reconstruction. The work is promising for future studies involving databases of anatomical atlases.