Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

Author name not available (Why is that?)

Publication date: 28 March 2021

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.

Has companion code repository: https://github.com/wherzberg/Graph-Convolutional-Newton-type-Method

This page was built for publication: Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6363930)