Beltrami-Net: Domain Independent Deep D-bar Learning for Absolute Imaging with Electrical Impedance Tomography (a-EIT)
This work addresses a key challenge in EIT by enabling more general networks without boundary shape specificity, which is promising for applications like anatomical atlases, though it appears incremental as it builds on existing D-bar and deep learning techniques.
The authors tackled absolute Electrical Impedance Tomography (a-EIT) image reconstruction by pairing a D-bar method with a CNN trained on boundary shape-independent simulated data, resulting in significant improvements in image quality measured by SSIMs and relative ℓ₂/ℓ₁ errors on experimental data from two EIT systems.
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.