@article{discovery10139975,
           title = {Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems},
            year = {2021},
       publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
         journal = {IEEE Transactions on Computational Imaging},
           month = {December},
            note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.},
        keywords = {Finite element method, graph convolutional
networks, model-based deep learning, conductivity, electrical
impedance tomography.},
        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.},
          author = {Herzberg, W and Rowe, D and Hauptmann, A and Hamilton, S},
             url = {http://dx.doi.org/10.1109/TCI.2021.3132190}
}