# Compressed Sensing with Deep Image Prior and Learned Regularization

arXiv: https://arxiv.org/abs/1806.06438 · HTML: https://mlsanity.com/paper/1806.06438/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2018.

## Built on by (most cited first, 30 of 47)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Auditing Privacy Defenses in Federated Learning via Generative Gradient Leakage](https://mlsanity.com/paper/2203.15696/) (2022)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)
- [ZeroRF: Fast Sparse View 360deg Reconstruction with Zero Pretraining](https://mlsanity.com/paper/2312.09249/) (2023)
- [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)
- [Data augmentation for deep learning based accelerated MRI reconstruction with limited data](https://mlsanity.com/paper/2106.14947/) (2021)
- [Understanding Overparameterization in Generative Adversarial Networks](https://mlsanity.com/paper/2104.05605/) (2021)
- [Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors](https://mlsanity.com/paper/2106.15358/) (2021)
- [Untrained networks for compressive lensless photography](https://mlsanity.com/paper/2103.07609/) (2021)
- [Adaptive Compressed Sensing with Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2407.08256/) (2024)
- [Generative Principal Component Analysis](https://mlsanity.com/paper/2203.09693/) (2022)
- [Non-Iterative Recovery from Nonlinear Observations using Generative Models](https://mlsanity.com/paper/2205.15749/) (2022)
- [Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors](https://mlsanity.com/paper/2108.03570/) (2021)
- [Computational Imaging and Artificial Intelligence: The Next Revolution of Mobile Vision](https://mlsanity.com/paper/2109.08880/) (2021)
- [Misspecified Phase Retrieval with Generative Priors](https://mlsanity.com/paper/2210.05571/) (2022)
- [Optimization for Amortized Inverse Problems](https://mlsanity.com/paper/2210.13983/) (2022)
- [Beyond Independent Measurements: General Compressed Sensing with GNN Application](https://mlsanity.com/paper/2111.00327/) (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)
- [Self-diffusion for Solving Inverse Problems](https://mlsanity.com/paper/2510.21417/) (2025)
- [Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models](https://mlsanity.com/paper/2112.03860/) (2021)
- [Nonlinear ill-posed problem in low-dose dental cone-beam computed tomography](https://mlsanity.com/paper/2303.01678/) (2023)
- [Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimation](https://mlsanity.com/paper/2404.05445/) (2024)
- [Generalized Eigenvalue Problems with Generative Priors](https://mlsanity.com/paper/2411.01326/) (2024)
- [Scale-Agnostic Super-Resolution in MRI using Feature-Based Coordinate Networks](https://mlsanity.com/paper/2210.08676/) (2022)
- [RDFNet: Regional Dynamic FISTA-Net for Spectral Snapshot Compressive Imaging](https://mlsanity.com/paper/2302.02519/) (2023)
- [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)

## Abstract (arXiv)

We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match the observed measurements. We show that this approach can be applied to solve any differentiable linear inverse problem, outperforming previous unlearned methods. Unlike various learned approaches based on generative models, our method does not require pre-training over large datasets. We further introduce a novel learned regularization technique, which incorporates prior information on the network weights. This reduces reconstruction error, especially for noisy measurements. Finally, we prove that, using the DIP optimization approach, moderately overparameterized single-layer networks can perfectly fit any signal despite the non-convex nature of the fitting problem. This theoretical result provides justification for early stopping.