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PreprintCC BY 4.0arXiv

i-DEQ: A stable inertial deep equilibrium model for image restoration

  • Antonin Clerc
  • Marien Renaud
  • Baudouin Denis De Senneville
  • Nicolas Papadakis
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Abstract

Deep Equilibrium Models (DEQs) are an established framework for image restoration that learn a problem-adapted regularization by solving a fixed-point (i.e. equilibrium) problem. While flexible and expressive, DEQs are often hindered by high computational cost and training instability. We propose an inertial DEQ (i-DEQ) that learns an explicit nonconvex regularization within the DEQ formulation. By using momentum within the fixed-point iterations, i-DEQ has convergence guarantees and accelerated rates. Moreover, we observe that i-DEQ is significantly more stable during the training and robust to rough initialization than DEQs. Numerical experiments on various linear and nonlinear inverse problems demonstrate that i-DEQ achieves reconstruction quality comparable to state-of-the-art methods, while reducing DEQ's inference time by a factor of two.

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Cite

BibTeXRIS
BibTeX
@misc{clerc2026ideq,
  title = {{i-DEQ: A stable inertial deep equilibrium model for image restoration}},
  author = {Antonin Clerc and Marien Renaud and Baudouin Denis De Senneville and Nicolas Papadakis},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.19705},
  eprint = {2605.19705},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.19705},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - i-DEQ: A stable inertial deep equilibrium model for image restoration
AU  - Antonin Clerc
AU  - Marien Renaud
AU  - Baudouin Denis De Senneville
AU  - Nicolas Papadakis
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2605.19705
UR  - https://arxiv.org/abs/2605.19705
AB  - Deep Equilibrium Models (DEQs) are an established framework for image restoration that learn a problem-adapted regularization by solving a fixed-point (i.e. equilibrium) problem. While flexible and expressive, DEQs are often hindered by high computational cost and training instability. We propose an inertial DEQ (i-DEQ) that learns an explicit nonconvex regularization within the DEQ formulation. By using momentum within the fixed-point iterations, i-DEQ has convergence guarantees and accelerated rates. Moreover, we observe that i-DEQ is significantly more stable during the training and robust to rough initialization than DEQs. Numerical experiments on various linear and nonlinear inverse problems demonstrate that i-DEQ achieves reconstruction quality comparable to state-of-the-art methods, while reducing DEQ's inference time by a factor of two.
ER  -