University of Oulu

Arridge, S., Hauptmann, A. Networks for Nonlinear Diffusion Problems in Imaging. J Math Imaging Vis 62, 471–487 (2020).

Networks for nonlinear diffusion problems in imaging

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Author: Arridge, S.1; Hauptmann, A.1,2
Organizations: 1Department of Computer Science, University College London, London, UK
2Research Unit of Mathematical Sciences, University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 2.5 MB)
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Language: English
Published: Springer Nature, 2020
Publish Date: 2019-10-14


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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Series: Journal of mathematical imaging and vision
ISSN: 0924-9907
ISSN-E: 1573-7683
ISSN-L: 0924-9907
Volume: 62
Pages: 471 - 487
DOI: 10.1007/s10851-019-00901-3
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: Open access funding provided by University of Oulu including Oulu University Hospital. We thank Jonas Adler and Sebastian Lunz for valuable discussions and comments.
Copyright information: © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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.