University of Oulu

Hamilton, S. J., Hänninen, A., Hauptmann, A., & Kolehmainen, V. (2019). Beltrami-net: domain-independent deep D-bar learning for absolute imaging with electrical impedance tomography (a-EIT). Physiological Measurement, 40(7), 74002.

Beltrami-net : domain-independent deep D-bar learning for absolute imaging with electrical impedance tomography (a-EIT)

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Author: Hamilton, S J1; Hänninen, A2; Hauptmann, A3,4;
Organizations: 1Department of Mathematics, Statistics, and Computer Science, Marquette University, Milwaukee, WI 53233, United States of America
2Department of Applied Physics, University of Eastern Finland, Kuopio, Finland
3Research Unit of Mathematical Sciences, University of Oulu, Oulu, Finland
4Department of Computer Science, University College London, London, United Kingdom
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 3.3 MB)
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Language: English
Published: IOP Publishing, 2019
Publish Date: 2019-08-19


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 and examine the influence of prior information on the reconstruction.

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) with separate training sets of varying prior information.

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 ℓ₂ and ℓ₁ 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.

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Series: Physiological measurement
ISSN: 0967-3334
ISSN-E: 1361-6579
ISSN-L: 0967-3334
Volume: 40
Issue: 7
Article number: 074002
DOI: 10.1088/1361-6579/ab21b2
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
113 Computer and information sciences
217 Medical engineering
Funding: We acknowledge the support of NVIDIA Corporation for the donation of the Titan Xp GPU used for this research. This work was supported by the Academy of Finland (Project 312343 and 312123, Finnish Centre of Excellence in Inverse Modelling and Imaging, 2018–2025). A Hänninen and V Kolehmainen acknowledge support by the Jane and Aatos Erkko Foundation. A Hauptmann was supported by the Wellcome-EPSRC project NS/A000027/1. SH was supported by the National Institute Of Biomedical Imaging And Bioengineering of the National Institutes of Health under Award Number R21EB028064. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
Academy of Finland Grant Number: 312343
Detailed Information: 312343 (Academy of Finland Funding decision)
312123 (Academy of Finland Funding decision)
Copyright information: © 2019 Institute of Physics and Engineering in Medicine. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.