# Fast Equivariant Imaging: Accelerating Unsupervised Learning and Model Adaptation via Inexact Splitting

arXiv: https://arxiv.org/abs/2507.06764 · HTML: https://mlsanity.com/paper/2507.06764/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Fast Adaptation to Super-Resolution Networks via Meta-Learning](https://mlsanity.com/paper/2001.02905/) (2020)
- [Test-Time Training Can Close the Natural Distribution Shift Performance Gap in Deep Learning Based Compressed Sensing](https://mlsanity.com/paper/2204.07204/) (2022)
- [Maximal Sparsity with Deep Networks?](https://mlsanity.com/paper/1605.01636/) (2016)
- [Equivariant plug-and-play image reconstruction](https://mlsanity.com/paper/2312.01831/) (2023)
- [Unsupervised Learning From Incomplete Measurements for Inverse Problems](https://mlsanity.com/paper/2201.12151/) (2022)
- [Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting](https://mlsanity.com/paper/2011.01748/) (2020)
- [Provably Convergent Plug-and-Play Quasi-Newton Methods](https://mlsanity.com/paper/2303.07271/) (2023)
- [Inexact Block Coordinate Descent Algorithms for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1905.04211/) (2019)
- [Truly shift-equivariant convolutional neural networks with adaptive polyphase upsampling](https://mlsanity.com/paper/2105.04040/) (2021)
- [Self-supervised Deep Unrolled Reconstruction Using Regularization by Denoising](https://mlsanity.com/paper/2205.03519/) (2022)
- [Deep Unrolling Networks with Recurrent Momentum Acceleration for Nonlinear Inverse Problems](https://mlsanity.com/paper/2307.16120/) (2023)
- [A Guide to Stochastic Optimisation for Large-Scale Inverse Problems](https://mlsanity.com/paper/2406.06342/) (2024)

## Abstract (arXiv)

In this work, we propose Fast Equivariant Imaging (FEI), a novel unsupervised learning framework to rapidly and efficiently train deep imaging networks without ground-truth data. FEI reformulates the EI objective through an inexact variable-splitting scheme, decoupling network training from an auxiliary restoration step implemented with a plug-and-play denoiser, this novel unsupervised scheme shows superior efficiency and performance compared to the standard Equivariant Imaging paradigm. In particular, our FEI schemes achieve an order-of-magnitude (10x) acceleration over standard EI on training U-Net for X-ray CT reconstruction and image inpainting, with improved generalization performance. Beyond offline training, the proposed scheme also enables efficient test-time adaptation of a pretrained model to individual samples, to secure further performance improvements. Extensive experiments show that the proposed approach provides a noticeable efficiency and performance gain over existing unsupervised methods and model adaptation techniques.