eprintid: 10139975
rev_number: 15
eprint_status: archive
userid: 608
dir: disk0/10/13/99/75
datestamp: 2021-12-09 15:24:33
lastmod: 2021-12-09 15:25:13
status_changed: 2021-12-09 15:25:13
type: article
metadata_visibility: show
creators_name: Herzberg, W
creators_name: Rowe, D
creators_name: Hauptmann, A
creators_name: Hamilton, S
title: Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems
ispublished: pub
divisions: UCL
divisions: B04
divisions: C05
divisions: F48
keywords: Finite element method, graph convolutional
networks, model-based deep learning, conductivity, electrical
impedance tomography.
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: 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 strong 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.
date: 2021-12-02
date_type: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
official_url: http://dx.doi.org/10.1109/TCI.2021.3132190
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1908768
doi: 10.1109/tci.2021.3132190
lyricists_name: Hauptmann, Andreas
lyricists_id: AHAUP49
actors_name: Hauptmann, Andreas
actors_id: AHAUP49
actors_role: owner
full_text_status: public
publication: IEEE Transactions on Computational Imaging
citation:        Herzberg, W;    Rowe, D;    Hauptmann, A;    Hamilton, S;      (2021)    Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems.                   IEEE Transactions on Computational Imaging        10.1109/tci.2021.3132190 <https://doi.org/10.1109/tci.2021.3132190>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10139975/1/2021_Herzberg_preprint.pdf