DREAM: Deep-Reparametrization of Adaptive Regularization Maps for Fast Zero-Shot Self-Supervised Learning

Abstract

Adaptive regularization is an effective means of improving the flexibility of classical variational reconstruction methods while retaining their interpretability and mathematical structure. In this work, we propose an approach for learning deep-reparameterized adaptive regularization maps (DREAM) for Total Variation (TV) and Total Generalized Variation (TGV) through algorithm unrolling in a zero-shot, self-supervised setting, requiring no access to large paired datasets. We first validate DREAM on a two-dimensional image-denoising problem and then apply it to large-scale dynamic MRI reconstruction. The resulting adaptive models are theoretically grounded, as they retain the convergence properties of the primal-dual algorithm used as the building block of the unrolled architecture. Our results show that the regularization parameter maps can be learned efficiently, requiring substantially fewer weight updates than state-of-the-art methods to achieve comparable performance. We further demonstrate that the CNN parametrization of the maps acts as an implicit prior and provides effective dimensionality reduction, outperforming direct optimization of the adaptive parameters. Across both applications, the performance gap between supervised and zero-shot training is smaller for DREAM than for the end-to-end deep-learning methods considered for comparison. Remarkably, in dynamic cardiac MRI reconstruction, zero-shot training matches the performance of the supervised model. Moreover, the learned adaptive maps are highly interpretable, providing a compelling alternative to purely deep-learning-based methods when reference data are difficult to obtain.

Phase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization
Xiaoxin Huang, Masayuki Ohzeki
arXiv15 Sep 2026PreprintarXiv licenceFull textGeneral mathematics Quantum physics & quantum informationarXiv
Sparse Signal Recovery Using Log-Sum Regularization and Adaptive Smoothing
Keisuke Morita, Masayuki Ohzeki
arXiv3 Sep 2026PreprintCC BY 4.0Full textGeneral mathematicsarXiv
Adaptive Regularization via Extreme Value Distributions for Gaussian Graphical Models
Alexander P. Christensen, Jeongwon Choi, Haoyi Yang +1
arXiv4 Sep 2026PreprintCC BY 4.0Full textStatisticsarXiv
Blockwise Stabilized Adaptive Cubic Regularization with Subsolvers via Recurrence
Rodion Podorozhny
arXiv14 Oct 2026PreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
Difference-of-Convex Regularization for Graph Learning by Differentiable Programming
Liping Tao, Chee Wei Tan
arXiv4 Oct 2026PreprintarXiv licenceFull textOptimisation & controlarXiv

Cite

BibTeX RIS

BibTeX

@misc{vu2026dream,
  title = {{DREAM: Deep-Reparametrization of Adaptive Regularization Maps for Fast Zero-Shot Self-Supervised Learning}},
  author = {Thanh Trung Vu and Ander Biguri and Christoph Kolbitsch and Luca Calatroni and Kostas Papafitsoros and Andreas Kofler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04019},
  eprint = {2609.04019},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04019},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - DREAM: Deep-Reparametrization of Adaptive Regularization Maps for Fast Zero-Shot Self-Supervised Learning
AU  - Thanh Trung Vu
AU  - Ander Biguri
AU  - Christoph Kolbitsch
AU  - Luca Calatroni
AU  - Kostas Papafitsoros
AU  - Andreas Kofler
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04019
UR  - https://arxiv.org/abs/2609.04019
AB  - Adaptive regularization is an effective means of improving the flexibility of classical variational reconstruction methods while retaining their interpretability and mathematical structure. In this work, we propose an approach for learning deep-reparameterized adaptive regularization maps (DREAM) for Total Variation (TV) and Total Generalized Variation (TGV) through algorithm unrolling in a zero-shot, self-supervised setting, requiring no access to large paired datasets. We first validate DREAM on a two-dimensional image-denoising problem and then apply it to large-scale dynamic MRI reconstruction. The resulting adaptive models are theoretically grounded, as they retain the convergence properties of the primal-dual algorithm used as the building block of the unrolled architecture. Our results show that the regularization parameter maps can be learned efficiently, requiring substantially fewer weight updates than state-of-the-art methods to achieve comparable performance. We further demonstrate that the CNN parametrization of the maps acts as an implicit prior and provides effective dimensionality reduction, outperforming direct optimization of the adaptive parameters. Across both applications, the performance gap between supervised and zero-shot training is smaller for DREAM than for the end-to-end deep-learning methods considered for comparison. Remarkably, in dynamic cardiac MRI reconstruction, zero-shot training matches the performance of the supervised model. Moreover, the learned adaptive maps are highly interpretable, providing a compelling alternative to purely deep-learning-based methods when reference data are difficult to obtain.
ER  -

Abstract

Related

Cite