Arridge, S;
Hauptmann, A;
(2019)
Networks for Nonlinear Diffusion Problems in Imaging.
Journal of Mathematical Imaging and Vision
10.1007/s10851-019-00901-3.
(In press).
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Abstract
A multitude of imaging and vision tasks have seen recently a major transformation by deep learning methods and in particular by the application of convolutional neural networks. These methods achieve impressive results, even for applications where it is not apparent that convolutions are suited to capture the underlying physics. In this work we develop a network architecture based on nonlinear diffusion processes, named DiffNet. By design, we obtain a nonlinear network architecture that is well suited for diffusion related problems in imaging. Furthermore, the performed updates are explicit, by which we obtain better interpretability and generalisability compared to classical convolutional neural network architectures. The performance of DiffNet tested on the inverse problem of nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset. We obtain competitive results to the established U-Net architecture, with a fraction of parameters and necessary training data.
| Type: | Article |
|---|---|
| Title: | Networks for Nonlinear Diffusion Problems in Imaging |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10851-019-00901-3 |
| Publisher version: | https://doi.org/10.1007/s10851-019-00901-3 |
| Language: | English |
| Additional information: | Copyright © The Author(s) 2019, Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Neural networks · Deep learning · Partial differential equations · Nonlinear diffusion · Image flow · Nonlinear inverse problems |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10083233 |
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