# Equivariance Regularization for Image Reconstruction

arXiv: https://arxiv.org/abs/2202.05062 · HTML: https://mlsanity.com/paper/2202.05062/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 18 of 18)

- [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 Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Katyusha: The First Direct Acceleration of Stochastic Gradient Methods](https://mlsanity.com/paper/1603.05953/) (2016)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
- [Randomized Sketches of Convex Programs with Sharp Guarantees](https://mlsanity.com/paper/1404.7203/) (2014)
- [The Practicality of Stochastic Optimization in Imaging Inverse Problems](https://mlsanity.com/paper/1910.10100/) (2019)
- [Sharp Time--Data Tradeoffs for Linear Inverse Problems](https://mlsanity.com/paper/1507.04793/) (2015)
- [Gradient Projection Iterative Sketch for Large-Scale Constrained Least-Squares](https://mlsanity.com/paper/1609.09419/) (2016)
- [Stochastic Primal-Dual Deep Unrolling](https://mlsanity.com/paper/2110.10093/) (2021)
- [Rest-Katyusha: Exploiting the Solution's Structure via Scheduled Restart Schemes](https://mlsanity.com/paper/1803.02246/) (2018)
- [Linear Convergence of SVRG in Statistical Estimation](https://mlsanity.com/paper/1611.01957/) (2016)

## Built on by (most cited first, 1 of 1)

- [Drawback of Enforcing Equivariance and its Compensation via the Lens of Expressive Power](https://mlsanity.com/paper/2512.09673/) (2025)

## Abstract (arXiv)

In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant structure in the physics of the measurements -- which is prevalent in many inverse problems such as tomographic image reconstruction -- to mitigate the ill-poseness of the inverse problem. Our proposed scheme can be applied in a plug-and-play manner alongside with any classic first-order optimization algorithm such as the accelerated gradient descent/FISTA for simplicity and fast convergence. The numerical experiments in sparse-view X-ray CT image reconstruction tasks demonstrate the effectiveness of our approach.