DEALing with Image Reconstruction: Deep Attentive Least Squares

Mehrsa Pourya, Erich Kobler, Michael Unser, Sebastian Neumayer
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:49689-49708, 2025.

Abstract

State-of-the-art image reconstruction often relies on complex, abundantly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively refines intermediate reconstructions by solving a sequence of quadratic problems. These updates have two key components: (i) learned filters to extract salient image features; and (ii) an attention mechanism that locally adjusts the penalty of the filter responses. Our method matches leading plug-and-play and learned regularizer approaches in performance while offering interpretability, robustness, and convergent behavior. In effect, we bridge traditional regularization and deep learning with a principled reconstruction approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-pourya25a, title = {{DEAL}ing with Image Reconstruction: Deep Attentive Least Squares}, author = {Pourya, Mehrsa and Kobler, Erich and Unser, Michael and Neumayer, Sebastian}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {49689--49708}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/pourya25a/pourya25a.pdf}, url = {https://proceedings.mlr.press/v267/pourya25a.html}, abstract = {State-of-the-art image reconstruction often relies on complex, abundantly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively refines intermediate reconstructions by solving a sequence of quadratic problems. These updates have two key components: (i) learned filters to extract salient image features; and (ii) an attention mechanism that locally adjusts the penalty of the filter responses. Our method matches leading plug-and-play and learned regularizer approaches in performance while offering interpretability, robustness, and convergent behavior. In effect, we bridge traditional regularization and deep learning with a principled reconstruction approach.} }
Endnote
%0 Conference Paper %T DEALing with Image Reconstruction: Deep Attentive Least Squares %A Mehrsa Pourya %A Erich Kobler %A Michael Unser %A Sebastian Neumayer %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-pourya25a %I PMLR %P 49689--49708 %U https://proceedings.mlr.press/v267/pourya25a.html %V 267 %X State-of-the-art image reconstruction often relies on complex, abundantly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively refines intermediate reconstructions by solving a sequence of quadratic problems. These updates have two key components: (i) learned filters to extract salient image features; and (ii) an attention mechanism that locally adjusts the penalty of the filter responses. Our method matches leading plug-and-play and learned regularizer approaches in performance while offering interpretability, robustness, and convergent behavior. In effect, we bridge traditional regularization and deep learning with a principled reconstruction approach.
APA
Pourya, M., Kobler, E., Unser, M. & Neumayer, S.. (2025). DEALing with Image Reconstruction: Deep Attentive Least Squares. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:49689-49708 Available from https://proceedings.mlr.press/v267/pourya25a.html.

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