Equivariant Deep Equilibrium Models for Imaging Inverse Problems
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Abstract (arXiv)
Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed point of a learned operator. However, training DEQs with complex EI losses requires implicit differentiation through fixed-point computations, whose implementation can be challenging. We show that backpropagation can be implemented modularly, simplifying training. Experiments demonstrate that DEQs trained with implicit differentiation outperform those trained with Jacobian-free backpropagation and other baseline methods. Additionally, we find evidence that EI-trained DEQs approximate the proximal map of an invariant prior.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 21 of its 29 references that are in the map. First posted on arXiv 24 Nov 2025.
Builds on
21 of 29 references.
References · 21
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
- 2018Group Normalizationcited by 1,524
- 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,358
- 2019Deep Equilibrium Modelscited by 615
- 2016Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networkscited by 543
- 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 470
- 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 307
- 2017A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstructioncited by 232
- 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 198
- 2021Deep Equilibrium Architectures for Inverse Problems in Imagingcited by 127
- 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 108
- 2021JFB: Jacobian-Free Backpropagation for Implicit Networkscited by 86
9 more
- 2021Equivariant Imaging: Learning Beyond the Range Spacecited by 83
- 2022Physics-Driven Deep Learning for Computational Magnetic Resonance Imagingcited by 50
- 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 41
- 2021Equivariant neural networks for inverse problemscited by 29
- 2025DeepInverse: A Python package for solving imaging inverse problems with deep learningcited by 28
- 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 25
- 2023TorchDEQ: A Library for Deep Equilibrium Modelscited by 21
- 2023Deep Equilibrium Learning of Explicit Regularizers for Imaging Inverse Problemscited by 16
- 2022DEQ-MPI: A Deep Equilibrium Reconstruction with Learned Consistency for Magnetic Particle Imagingcited by 9
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Citing papers per year: 2026: 1.
1 paper.