# Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors

arXiv: https://arxiv.org/abs/1906.08763 · HTML: https://mlsanity.com/paper/1906.08763/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2019.

## Built on by (most cited first, 30 of 32)

- [Learned reconstruction methods with convergence guarantees](https://mlsanity.com/paper/2206.05431/) (2022)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [Fixed-Point and Objective Convergence of Plug-and-Play Algorithms](https://mlsanity.com/paper/2104.10348/) (2021)
- [Self-Validation: Early Stopping for Single-Instance Deep Generative Priors](https://mlsanity.com/paper/2110.12271/) (2021)
- [Provable Compressed Sensing with Generative Priors via Langevin Dynamics](https://mlsanity.com/paper/2102.12643/) (2021)
- [Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors](https://mlsanity.com/paper/2106.15358/) (2021)
- [Generative Principal Component Analysis](https://mlsanity.com/paper/2203.09693/) (2022)
- [Misspecified Phase Retrieval with Generative Priors](https://mlsanity.com/paper/2210.05571/) (2022)
- [Projected Gradient Descent Algorithms for Solving Nonlinear Inverse Problems with Generative Priors](https://mlsanity.com/paper/2209.10093/) (2022)
- [Phase Retrieval using Single-Instance Deep Generative Prior](https://mlsanity.com/paper/2106.04812/) (2021)
- [Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise](https://mlsanity.com/paper/2402.15635/) (2024)
- [Multilook Coherent Imaging: Theoretical Guarantees and Algorithms](https://mlsanity.com/paper/2505.23594/) (2025)
- [Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems](https://mlsanity.com/paper/2309.12128/) (2023)
- [Generalized Eigenvalue Problems with Generative Priors](https://mlsanity.com/paper/2411.01326/) (2024)
- [Learning Single Index Models with Diffusion Priors](https://mlsanity.com/paper/2505.21135/) (2025)
- [Non-Convex Compressed Sensing with Training Data](https://mlsanity.com/paper/2101.08310/) (2021)
- [Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models](https://mlsanity.com/paper/2105.06371/) (2021)
- [On the Fine-Grained Hardness of Inverting Generative Models](https://mlsanity.com/paper/2309.05795/) (2023)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Low-light phase retrieval with implicit generative priors](https://mlsanity.com/paper/2402.17745/) (2024)
- [Untrained Neural Nets for Snapshot Compressive Imaging: Theory and Algorithms](https://mlsanity.com/paper/2406.03694/) (2024)
- [DAEs for Linear Inverse Problems: Improved Recovery with Provable Guarantees](https://mlsanity.com/paper/2101.05130/) (2021)
- [A Note on Machine Learning Approach for Computational Imaging](https://mlsanity.com/paper/2202.11883/) (2022)
- [Learning Trees of ℓ0-Minimization Problems](https://mlsanity.com/paper/2302.02548/) (2023)
- [Linear Convergence of Reshuffling Kaczmarz Methods With Sparse Constraints](https://mlsanity.com/paper/2304.10123/) (2023)
- [Untrained neural network embedded Fourier phase retrieval from few measurements](https://mlsanity.com/paper/2307.08717/) (2023)
- [Imaging Signal Recovery Using Neural Network Priors Under Uncertain Forward Model Parameters](https://mlsanity.com/paper/2405.02944/) (2024)
- [Towards Lensless Image Deblurring with Prior-Embedded Implicit Neural Representations in the Low-Data Regime](https://mlsanity.com/paper/2411.18189/) (2024)

## Abstract (arXiv)

Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-rank. Unlike learned generative priors they do not require any training over large datasets. However, few theoretical guarantees exist in the scope of using untrained neural network priors for inverse imaging problems. We explore new applications and theory for untrained neural network priors. Specifically, we consider the problem of solving linear inverse problems, such as compressive sensing, as well as non-linear problems, such as compressive phase retrieval. We model images to lie in the range of an untrained deep generative network with a fixed seed. We further present a projected gradient descent scheme that can be used for both compressive sensing and phase retrieval and provide rigorous theoretical guarantees for its convergence. We also show both theoretically as well as empirically that with deep network priors, one can achieve better compression rates for the same image quality compared to hand crafted priors.