Networks for nonlinear diffusion problems in imaging
Arridge, S.; Hauptmann, A. (2019-09-13)
Arridge, S., Hauptmann, A. Networks for Nonlinear Diffusion Problems in Imaging. J Math Imaging Vis 62, 471–487 (2020). https://doi.org/10.1007/s10851-019-00901-3
© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.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.
https://creativecommons.org/licenses/by/4.0/
https://urn.fi/URN:NBN:fi-fe2019101432458
Tiivistelmä
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 is 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.
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