# Discovering Structure From Corruption for Unsupervised Image Reconstruction

arXiv: https://arxiv.org/abs/2304.05589 · HTML: https://mlsanity.com/paper/2304.05589/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 63 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Builds on (most cited first, 25 of 25)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [Trumpets: Injective Flows for Inference and Inverse Problems](https://mlsanity.com/paper/2102.10461/) (2021)
- [The Numerics of Phase Retrieval](https://mlsanity.com/paper/2004.05788/) (2020)
- [Task-Aware Compressed Sensing with Generative Adversarial Networks](https://mlsanity.com/paper/1802.01284/) (2018)
- [Consistency of Variational Bayes Inference for Estimation and Model Selection in Mixtures](https://mlsanity.com/paper/1805.05054/) (2018)
- [alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction](https://mlsanity.com/paper/2201.08506/) (2022)
- [Sparse Phase Retrieval: Convex Algorithms and Limitations](https://mlsanity.com/paper/1303.4128/) (2013)
- [Image Reconstruction without Explicit Priors](https://mlsanity.com/paper/2303.12217/) (2023)
- [Rate-Optimal Denoising with Deep Neural Networks](https://mlsanity.com/paper/1805.08855/) (2018)
- [Data-Driven Computational Imaging for Scientific Discovery](https://mlsanity.com/paper/2210.16709/) (2022)
- [A Self-Supervised Approach to Reconstruction in Sparse X-Ray Computed Tomography](https://mlsanity.com/paper/2211.00002/) (2022)

## Built on by (most cited first, 5 of 5)

- [Denoising Score Distillation: From Noisy Diffusion Pretraining to One-Step High-Quality Generation](https://mlsanity.com/paper/2503.07578/) (2025)
- [The Star Geometry of Critic-Based Regularizer Learning](https://mlsanity.com/paper/2408.16852/) (2024)
- [Double Blind Imaging with Generative Modeling](https://mlsanity.com/paper/2503.21501/) (2025)
- [Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Data](https://mlsanity.com/paper/2601.18728/) (2026)
- [MIRA: A Score for Conditional Distribution Accuracy and Model Comparison](https://mlsanity.com/paper/2605.02014/) (2026)

## Abstract (arXiv)

We consider solving ill-posed imaging inverse problems without access to an image prior or ground-truth examples. An overarching challenge in these inverse problems is that an infinite number of images, including many that are implausible, are consistent with the observed measurements. Thus, image priors are required to reduce the space of possible solutions to more desirable reconstructions. However, in many applications it is difficult or potentially impossible to obtain example images to construct an image prior. Hence inaccurate priors are often used, which inevitably result in biased solutions. Rather than solving an inverse problem using priors that encode the spatial structure of any one image, we propose to solve a set of inverse problems jointly by incorporating prior constraints on the collective structure of the underlying images. The key assumption of our work is that the underlying images we aim to reconstruct share common, low-dimensional structure. We show that such a set of inverse problems can be solved simultaneously without the use of a spatial image prior by instead inferring a shared image generator with a low-dimensional latent space. The parameters of the generator and latent embeddings are found by maximizing a proxy for the Evidence Lower Bound (ELBO). Once identified, the generator and latent embeddings can be combined to provide reconstructed images for each inverse problem. The framework we propose can handle general forward model corruptions, and we show that measurements derived from only a small number of ground-truth images (leqslant 150) are sufficient for image reconstruction. We demonstrate our approach on a variety of convex and non-convex inverse problems, including denoising, phase retrieval, and black hole video reconstruction.