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Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees

arXiv 1802.08406 ↗First posted 23 Feb 2018stat.ML cs.LGcited by 58

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Abstract (arXiv)

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor discriminative capability, while learning-based methods seldom provide concrete theoretical guarantees. In this work, we advocate the idea of replacing hand-crafted priors, such as sparsity, with a Generative Adversarial Network (GAN) to solve linear inverse problems such as compressive sensing. In particular, we propose a projected gradient descent (PGD) algorithm for effective use of GAN priors for linear inverse problems, and also provide theoretical guarantees on the rate of convergence of this algorithm. Moreover, we show empirically that our algorithm demonstrates superior performance over an existing method of leveraging GANs for compressive sensing.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Feb 2018.

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Citing papers per year: 2021: 16; 2022: 14; 2023: 8; 2024: 8; 2025: 8; 2026: 4.

58 papers.

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  1. 2021GAN Inversion: A Surveycited by 366
  2. 2021Intermediate Layer Optimization for Inverse Problems using Deep Generative Modelscited by 70
  3. 2023Training-free Linear Image Inverses via Flowscited by 70
  4. 2021Trumpets: Injective Flows for Inference and Inverse Problemscited by 36
  5. 2022Bringing Your Own View: Graph Contrastive Learning without Prefabricated Data Augmentationscited by 28
  6. 2021Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Priorcited by 24
  7. 2021Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Conditioncited by 22
  8. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  9. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  10. 2025Personalized Image Generation with Deep Generative Models: A Decade Surveycited by 20
  11. 2022Unsupervised vocal dereverberation with diffusion-based generative modelscited by 18
  12. 2025Solving Inverse Problems with FLAIRcited by 16
38 more
  1. 2021Provable Compressed Sensing with Generative Priors via Langevin Dynamicscited by 14
  2. 2021Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priorscited by 14
  3. 2021ExSinGAN: Learning an Explainable Generative Model from a Single Imagecited by 12
  4. 2022Generative Principal Component Analysiscited by 12
  5. 2024CoSIGN: Few-Step Guidance of ConSIstency Model to Solve General INverse Problemscited by 12
  6. 2022Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priorscited by 9
  7. 2022Non-Iterative Recovery from Nonlinear Observations using Generative Modelscited by 9
  8. 2021Generalization Error of GAN from the Discriminator's Perspectivecited by 8
  9. 2022Misspecified Phase Retrieval with Generative Priorscited by 7
  10. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  11. 2023Inverse problem regularization with hierarchical variational autoencoderscited by 6
  12. 2024Paired Autoencoders for Likelihood-free Estimation in Inverse Problemscited by 6
  13. 2022Projected Gradient Descent Algorithms for Solving Nonlinear Inverse Problems with Generative Priorscited by 5
  14. 2024Particle-Filtering-based Latent Diffusion for Inverse Problemscited by 5
  15. 2022FunkNN: Neural Interpolation for Functional Generationcited by 4
  16. 2023JoIN: Joint GANs Inversion for Intrinsic Image Decompositioncited by 4
  17. 2023Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priorscited by 4
  18. 2023Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imagingcited by 4
  19. 2024Injectivity capacity of ReLU gatescited by 4
  20. 2024Generalized Eigenvalue Problems with Generative Priorscited by 3
  21. 2025DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealingcited by 3
  22. 2021On the Design of Deep Priors for Unsupervised Audio Restorationcited by 2
  23. 2025How many measurements are enough? Bayesian recovery in inverse problems with general distributionscited by 2
  24. 2025Learning Single Index Models with Diffusion Priorscited by 2
  25. 2026Error Analysis of Bayesian Inverse Problems with Generative Priorscited by 2
  26. 2021Provably Convergent Algorithms for Solving Inverse Problems Using Generative Modelscited by 1
  27. 2021Learning Generative Prior with Latent Space Sparsity Constraintscited by 1
  28. 2022A Survey on Leveraging Pre-trained Generative Adversarial Networks for Image Editing and Restorationcited by 1
  29. 2022Residual Back Projection With Untrained Neural Networkscited by 1
  30. 2023On the Fine-Grained Hardness of Inverting Generative Modelscited by 1
  31. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  32. 2024Enhancing and Accelerating Diffusion-Based Inverse Problem Solving through Measurements Optimizationcited by 1
  33. 2025Projection-Based Correction for Enhancing Deep Inverse Networkscited by 1
  34. 2026Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Frameworkcited by 1
  35. 2021DAEs for Linear Inverse Problems: Improved Recovery with Provable Guaranteescited by 0
  36. 2021Reconstructing Images of Two Adjacent Objects through Scattering Medium Using Generative Adversarial Networkcited by 0
  37. 2021Solving Inverse Problems with Conditional-GAN Prior via Fast Network-Projected Gradient Descentcited by 0
  38. 2022A Note on Machine Learning Approach for Computational Imagingcited by 0

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