Networks for Nonlinear Diffusion Problems in Imaging
This work addresses diffusion problems in imaging for computer vision researchers, offering an interpretable and efficient alternative to convolutional neural networks, though it is incremental as it builds on existing diffusion methods.
The authors tackled the problem of applying deep learning to diffusion-related imaging tasks by developing DiffNet, a network architecture based on nonlinear diffusion processes, which achieved competitive results to U-Net on the STL-10 dataset while using fewer parameters and less training data.
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.