# Scale-Equivariant Imaging: Self-Supervised Learning for Image Super-Resolution and Deblurring

arXiv: https://arxiv.org/abs/2312.11232 · HTML: https://mlsanity.com/paper/2312.11232/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 60 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [DDFM: Denoising Diffusion Model for Multi-Modality Image Fusion](https://mlsanity.com/paper/2303.06840/) (2023)
- [Neural Blind Deconvolution Using Deep Priors](https://mlsanity.com/paper/1908.02197/) (2019)
- [Equivariant Multi-Modality Image Fusion](https://mlsanity.com/paper/2305.11443/) (2023)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Practical Blind Image Denoising via Swin-Conv-UNet and Data Synthesis](https://mlsanity.com/paper/2203.13278/) (2022)
- [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)
- [Discrete Cosine Transform Network for Guided Depth Map Super-Resolution](https://mlsanity.com/paper/2104.06977/) (2021)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Unsupervised Learning with Stein's Unbiased Risk Estimator](https://mlsanity.com/paper/1805.10531/) (2018)
- [Sensing Theorems for Unsupervised Learning in Linear Inverse Problems](https://mlsanity.com/paper/2203.12513/) (2022)
- [Nonlinear Equivariant Imaging: Learning Multi-Parametric Tissue Mapping without Ground Truth for Compressive Quantitative MRI](https://mlsanity.com/paper/2211.12786/) (2022)

## Built on by (most cited first, 14 of 14)

- [Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data](https://mlsanity.com/paper/2403.08728/) (2024)
- [Perspective-Equivariance for Unsupervised Imaging with Camera Geometry](https://mlsanity.com/paper/2403.09327/) (2024)
- [Equivariant Imaging for Self-supervised Hyperspectral Image Inpainting](https://mlsanity.com/paper/2404.13159/) (2024)
- [Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimation](https://mlsanity.com/paper/2404.05445/) (2024)
- [EquiReg: Equivariance Regularized Diffusion for Inverse Problems](https://mlsanity.com/paper/2505.22973/) (2025)
- [Self-supervised conformal prediction for uncertainty quantification in Poisson imaging problems](https://mlsanity.com/paper/2502.19194/) (2025)
- [Equivariant Splitting: Self-supervised learning from incomplete data](https://mlsanity.com/paper/2510.00929/) (2025)
- [SHARE: A Fully Unsupervised Framework for Single Hyperspectral Image Restoration](https://mlsanity.com/paper/2601.13987/) (2026)
- [Equivariant Test-Time Training with Operator Sketching for Imaging Inverse Problems](https://mlsanity.com/paper/2411.05771/) (2024)
- [Learning to reconstruct from saturated data: audio declipping and high-dynamic range imaging](https://mlsanity.com/paper/2602.22279/) (2026)
- [UNet-AF: Alias-free UNet architectures](https://mlsanity.com/paper/2603.11323/) (2026)
- [Self-Supervised Super-Resolution for Sentinel-5P Hyperspectral Images](https://mlsanity.com/paper/2604.17652/) (2026)
- [Frozen CLIP Priors for Robust Self-Supervised Poisson Inverse Problems](https://mlsanity.com/paper/2608.20524/) (2026)
- [Hyperspectral Diffusion Equivariant Imaging (HyDiff-EI): A Self-supervised Framework for Hyperspectral Image Inpainting](https://mlsanity.com/paper/2608.26812/) (2026)

## Abstract (arXiv)

Self-supervised methods have recently proved to be nearly as effective as supervised ones in various imaging inverse problems, paving the way for learning-based approaches in scientific and medical imaging applications where ground truth data is hard or expensive to obtain. These methods critically rely on invariance to translations and/or rotations of the image distribution to learn from incomplete measurement data alone. However, existing approaches fail to obtain competitive performances in the problems of image super-resolution and deblurring, which play a key role in most imaging systems. In this work, we show that invariance to roto-translations is insufficient to learn from measurements that only contain low-frequency information. Instead, we propose scale-equivariant imaging, a new self-supervised approach that leverages the fact that many image distributions are approximately scale-invariant, enabling the recovery of high-frequency information lost in the measurement process. We demonstrate throughout a series of experiments on real datasets that the proposed method outperforms other self-supervised approaches, and obtains performances on par with fully supervised learning.