Graph convolutional networks enable fast hemorrhagic stroke monitoring with electrical impedance tomography

Objective: To develop a fast image reconstruction method for stroke monitoring with electrical impedance tomography with image quality comparable to computationally expensive nonlinear model-based methods. Methods: A post-processing approach with graph convolutional networks is employed. Utilizing the flexibility of the graph setting, a graph U-net is trained on linear difference reconstructions from 2D simulated stroke data and applied to fully 3D images from realistic simulated and experimental data. An additional network, trained on 3D vs. 2D images, is also considered for comparison. Results: Post-processing the linear difference reconstructions through the graph U-net significantly improved the image quality, resulting in images comparable to, or better than, the time-intensive nonlinear reconstruction method (a few minutes vs. several hours). Conclusion: Pairing a fast reconstruction method, such as linear difference imaging, with post-processing through a graph U-net provided significant improvements, at a negligible computational cost. Training in the graph framework vs classic pixel-based setting (CNN) allowed the ability to train on 2D cross-sectional images and process 3D volumes providing a nearly 50x savings in data simulation costs with no noticeable loss in quality. Significance: The proposed approach of post-processing a linear difference reconstruction with the graph U-net could be a feasible approach for on-line monitoring of hemorrhagic stroke.

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

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.