Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graph Convolutional Networks for Model-Based Learning in Nonlinear
  Inverse Problems   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.

20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph