Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction

Stanislas Ducotterd, Sebastian Neumayer, Michael Unser
Conference on Parsimony and Learning, PMLR 280:89-104, 2025.

Abstract

We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate the optimization as a bilevel problem. The inner problem deploys classical algorithms while the outer problem optimizes the dictionary and the regularizer parameters through supervised learning. The process is carried out via implicit differentiation and gradient-based optimization. We evaluate our method for denoising, super-resolution, and compressed-sensing magnetic-resonance imaging. We compare it to other classical models as well as deep-learning-based methods and show that it always outperforms the former and also the latter in some instances.

Cite this Paper

BibTeX
@InProceedings{pmlr-v280-ducotterd25a, title = {Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction}, author = {Ducotterd, Stanislas and Neumayer, Sebastian and Unser, Michael}, booktitle = {Conference on Parsimony and Learning}, pages = {89--104}, year = {2025}, editor = {Chen, Beidi and Liu, Shijia and Pilanci, Mert and Su, Weijie and Sulam, Jeremias and Wang, Yuxiang and Zhu, Zhihui}, volume = {280}, series = {Proceedings of Machine Learning Research}, month = {24--27 Mar}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v280/main/assets/ducotterd25a/ducotterd25a.pdf}, url = {https://proceedings.mlr.press/v280/ducotterd25a.html}, abstract = {We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate the optimization as a bilevel problem. The inner problem deploys classical algorithms while the outer problem optimizes the dictionary and the regularizer parameters through supervised learning. The process is carried out via implicit differentiation and gradient-based optimization. We evaluate our method for denoising, super-resolution, and compressed-sensing magnetic-resonance imaging. We compare it to other classical models as well as deep-learning-based methods and show that it always outperforms the former and also the latter in some instances.} }
Endnote
%0 Conference Paper %T Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction %A Stanislas Ducotterd %A Sebastian Neumayer %A Michael Unser %B Conference on Parsimony and Learning %C Proceedings of Machine Learning Research %D 2025 %E Beidi Chen %E Shijia Liu %E Mert Pilanci %E Weijie Su %E Jeremias Sulam %E Yuxiang Wang %E Zhihui Zhu %F pmlr-v280-ducotterd25a %I PMLR %P 89--104 %U https://proceedings.mlr.press/v280/ducotterd25a.html %V 280 %X We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate the optimization as a bilevel problem. The inner problem deploys classical algorithms while the outer problem optimizes the dictionary and the regularizer parameters through supervised learning. The process is carried out via implicit differentiation and gradient-based optimization. We evaluate our method for denoising, super-resolution, and compressed-sensing magnetic-resonance imaging. We compare it to other classical models as well as deep-learning-based methods and show that it always outperforms the former and also the latter in some instances.
APA
Ducotterd, S., Neumayer, S. & Unser, M.. (2025). Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction. Conference on Parsimony and Learning, in Proceedings of Machine Learning Research 280:89-104 Available from https://proceedings.mlr.press/v280/ducotterd25a.html.

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