# Image Reconstruction without Explicit Priors

arXiv: https://arxiv.org/abs/2303.12217 · HTML: https://mlsanity.com/paper/2303.12217/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (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)
- [Sparse Phase Retrieval: Convex Algorithms and Limitations](https://mlsanity.com/paper/1303.4128/) (2013)

## Built on by (most cited first, 8 of 8)

- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data](https://mlsanity.com/paper/2403.08728/) (2024)
- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Efficient Prior Calibration From Indirect Data](https://mlsanity.com/paper/2405.17955/) (2024)
- [Discovering Structure From Corruption for Unsupervised Image Reconstruction](https://mlsanity.com/paper/2304.05589/) (2023)
- [The Star Geometry of Critic-Based Regularizer Learning](https://mlsanity.com/paper/2408.16852/) (2024)
- [Optimizing Diffusion Priors in Image Reconstruction from a Single Observation](https://mlsanity.com/paper/2604.21066/) (2026)
- [Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem](https://mlsanity.com/paper/2609.03343/) (2026)

## Abstract (arXiv)

We consider solving ill-posed imaging inverse problems without access to an explicit image prior or ground-truth examples. An overarching challenge in inverse problems is that there are many undesired images that fit to the observed measurements, thus requiring image priors to constrain the space of possible solutions to more plausible reconstructions. However, in many applications it is difficult or potentially impossible to obtain ground-truth images to learn an image prior. Thus, inaccurate priors are often used, which inevitably result in biased solutions. Rather than solving an inverse problem using priors that encode the explicit 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 ground-truth images we aim to reconstruct share common, low-dimensional structure. We show that such a set of inverse problems can be solved simultaneously by learning a shared image generator with a low-dimensional latent space. The parameters of the generator and latent embedding are learned by maximizing a proxy for the Evidence Lower Bound (ELBO). Once learned, the generator and latent embeddings can be combined to provide reconstructions for each inverse problem. The framework we propose can handle general forward model corruptions, and we show that measurements derived from only a few ground-truth images (O(10)) are sufficient for image reconstruction without explicit priors.