Total Deep Variation for Linear Inverse Problems
Abstract
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We cast the learning problem as a discrete sampled optimal control problem, for which we derive the adjoint state equations and an optimality condition. By exploiting the variational structure of our approach, we perform a sensitivity analysis with respect to the learned parameters obtained from different training datasets. Moreover, we carry out a nonlinear eigenfunction analysis, which reveals interesting properties of the learned regularizer. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems.
Cite
Text
Kobler et al. "Total Deep Variation for Linear Inverse Problems." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020. doi:10.1109/CVPR42600.2020.00757Markdown
[Kobler et al. "Total Deep Variation for Linear Inverse Problems." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020.](https://mlanthology.org/cvpr/2020/kobler2020cvpr-total/) doi:10.1109/CVPR42600.2020.00757BibTeX
@inproceedings{kobler2020cvpr-total,
title = {{Total Deep Variation for Linear Inverse Problems}},
author = {Kobler, Erich and Effland, Alexander and Kunisch, Karl and Pock, Thomas},
booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2020},
doi = {10.1109/CVPR42600.2020.00757},
url = {https://mlanthology.org/cvpr/2020/kobler2020cvpr-total/}
}