University of Oulu

W. Herzberg, D. B. Rowe, A. Hauptmann and S. J. Hamilton, "Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems," in IEEE Transactions on Computational Imaging, vol. 7, pp. 1341-1353, 2021, doi: 10.1109/TCI.2021.3132190.

Graph convolutional networks for model-based learning in nonlinear inverse problems

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Author: Herzberg, William1; Rowe, Daniel B.1; Hauptmann, Andreas2,3;
Organizations: 1Department of Mathematical and Statistical Sciences; Marquette University, Milwaukee, WI 53233 USA
2Research Unit of Mathematical Sciences; University of Oulu, Oulu, Finland
3Department of Computer Science; University College London, London, United Kingdom
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 10.8 MB)
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Language: English
Published: Institute of Electrical and Electronics Engineers, 2021
Publish Date: 2021-12-14


The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has good generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training.

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Series: IEEE transactions on computational imaging
ISSN: 2573-0436
ISSN-E: 2333-9403
ISSN-L: 2573-0436
Volume: 7
Pages: 1341 - 1353
DOI: 10.1109/TCI.2021.3132190
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
113 Computer and information sciences
217 Medical engineering
Funding: This work was supported in part by National Institute Of Biomedical Imaging And Bioengineering of the National Institutes of Health under Award Number R21EB028064. The work of AH is supported by the Academy of Finland project numbers: 336796, 338408.
Academy of Finland Grant Number: 336796
Detailed Information: 336796 (Academy of Finland Funding decision)
338408 (Academy of Finland Funding decision)
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