mlsanityData to 14 Oct 2026

Compressed Sensing with Deep Image Prior and Learned Regularization

arXiv 1806.06438 ↗First posted 17 Jun 2018stat.ML cs.IT cs.LGcited by 47

Not on the map. Why?

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.

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

Builds on

No reference list yet.

Built on by

Cited by year

Citing papers per year: 2021: 17; 2022: 11; 2023: 6; 2024: 7; 2025: 6.

47 papers.

Sort:

By area:

  1. 2021Learning to Optimize: A Primer and A Benchmarkcited by 208
  2. 2022Auditing Privacy Defenses in Federated Learning via Generative Gradient Leakagecited by 72
  3. 2023Training-free Linear Image Inverses via Flowscited by 72
  4. 2021Early Stopping for Deep Image Priorcited by 44
  5. 2023ZeroRF: Fast Sparse View 360deg Reconstruction with Zero Pretrainingcited by 24
  6. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  7. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  8. 2021Data augmentation for deep learning based accelerated MRI reconstruction with limited datacited by 20
  9. 2021Understanding Overparameterization in Generative Adversarial Networkscited by 14
  10. 2021Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priorscited by 14
  11. 2021Untrained networks for compressive lensless photographycited by 13
  12. 2024Adaptive Compressed Sensing with Diffusion-Based Posterior Samplingcited by 13
35 more
  1. 2022Generative Principal Component Analysiscited by 12
  2. 2022Non-Iterative Recovery from Nonlinear Observations using Generative Modelscited by 9
  3. 2021Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priorscited by 7
  4. 2021Computational Imaging and Artificial Intelligence: The Next Revolution of Mobile Visioncited by 7
  5. 2022Misspecified Phase Retrieval with Generative Priorscited by 7
  6. 2022Optimization for Amortized Inverse Problemscited by 6
  7. 2021Beyond Independent Measurements: General Compressed Sensing with GNN Applicationcited by 5
  8. 2024Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noisecited by 4
  9. 2025Multilook Coherent Imaging: Theoretical Guarantees and Algorithmscited by 4
  10. 2025Self-diffusion for Solving Inverse Problemscited by 4
  11. 2021Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Modelscited by 3
  12. 2023Nonlinear ill-posed problem in low-dose dental cone-beam computed tomographycited by 3
  13. 2024Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimationcited by 3
  14. 2024Generalized Eigenvalue Problems with Generative Priorscited by 3
  15. 2022Scale-Agnostic Super-Resolution in MRI using Feature-Based Coordinate Networkscited by 2
  16. 2023RDFNet: Regional Dynamic FISTA-Net for Spectral Snapshot Compressive Imagingcited by 2
  17. 2025Learning Single Index Models with Diffusion Priorscited by 2
  18. 2021Non-Convex Compressed Sensing with Training Datacited by 1
  19. 2021Provably Convergent Algorithms for Solving Inverse Problems Using Generative Modelscited by 1
  20. 2022A Dataset-free Deep learning Method for Low-Dose CT Image Reconstructioncited by 1
  21. 2022MetaDIP: Accelerating Deep Image Prior with Meta Learningcited by 1
  22. 2022Residual Back Projection With Untrained Neural Networkscited by 1
  23. 2023Compressive Sensing with Tensorized Autoencodercited by 1
  24. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  25. 2025Comprehensive Examination of Unrolled Networks for Solving Linear Inverse Problemscited by 1
  26. 2025Deep Spectral Priorcited by 1
  27. 2025Diffusion Model Based Signal Recovery Under 1-Bit Quantizationcited by 1
  28. 2021Deep Chaos Synchronizationcited by 0
  29. 2021Generative Model Adversarial Training for Deep Compressed Sensingcited by 0
  30. 2021Variational framework for partially-measured physical system control: examples of vision neuroscience and optical random mediacited by 0
  31. 2021Using Deep Image Prior to Assist Variational Selective Segmentation Deep Learning Algorithmscited by 0
  32. 2022A Note on Machine Learning Approach for Computational Imagingcited by 0
  33. 2023Learning Trees of ℓ0-Minimization Problemscited by 0
  34. 2024Imaging Signal Recovery Using Neural Network Priors Under Uncertain Forward Model Parameterscited by 0
  35. 2024Towards Lensless Image Deblurring with Prior-Embedded Implicit Neural Representations in the Low-Data Regimecited by 0