mlsanityData to 14 Oct 2026

Misspecified Phase Retrieval with Generative Priors

arXiv 2210.05571 ↗First posted 11 Oct 2022stat.ML cs.LG eess.SPcited by 7

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Abstract (arXiv)

In this paper, we study phase retrieval under model misspecification and generative priors. In particular, we aim to estimate an n-dimensional signal x from m i.i.d.~realizations of the single index model y = f(aTx), where f is an unknown and possibly random nonlinear link function and a ∈ ℝn is a standard Gaussian vector. We make the assumption Cov[y,(aTx)2] ne 0, which corresponds to the misspecified phase retrieval problem. In addition, the underlying signal x is assumed to lie in the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. We propose a two-step approach, for which the first step plays the role of spectral initialization and the second step refines the estimated vector produced by the first step iteratively. We show that both steps enjoy a statistical rate of order √(klog L)· (log m)/m under suitable conditions. Experiments on image datasets are performed to demonstrate that our approach performs on par with or even significantly outperforms several competing methods.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 48 of its 103 references that are in the map. First posted on arXiv 11 Oct 2022.

Builds on

48 of 103 references.

References · 48

  1. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  2. 2020PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Modelscited by 358
  3. 2017Compressed Sensing using Generative Modelscited by 339
  4. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 291
  5. 2014Phase Retrieval via Wirtinger Flow: Theory and Algorithmscited by 125
  6. 2018Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networkscited by 120
  7. 2017Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Modelscited by 116
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  10. 2018Phase Retrieval Under a Generative Priorcited by 73
  11. 2018Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrievalcited by 71
  12. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
36 more
  1. 2013Phase Retrieval using Alternating Minimizationcited by 58
  2. 2018Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guaranteescited by 58
  3. 2015Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systemscited by 50
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  7. 2017Fundamental Limits of Weak Recovery with Applications to Phase Retrievalcited by 39
  8. 2020Phase retrieval in high dimensions: Statistical and computational phase transitionscited by 39
  9. 2017Global Guarantees for Enforcing Deep Generative Priors by Empirical Riskcited by 37
  10. 2019Bootstrapping Upper Confidence Boundcited by 36
  11. 2018Modeling Sparse Deviations for Compressed Sensing using Generative Modelscited by 33
  12. 2020Robust Compressed Sensing using Generative Modelscited by 33
  13. 2019Algorithmic Guarantees for Inverse Imaging with Untrained Network Priorscited by 32
  14. 2016Solving Systems of Random Quadratic Equations via Truncated Amplitude Flowcited by 29
  15. 2017Phase Transitions of Spectral Initialization for High-Dimensional Nonconvex Estimationcited by 26
  16. 2016PhaseMax: Convex Phase Retrieval via Basis Pursuitcited by 25
  17. 2019Information-Theoretic Lower Bounds for Compressive Sensing with Generative Modelscited by 25
  18. 2015Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flowcited by 23
  19. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  20. 2020Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priorscited by 21
  21. 2019Exact asymptotics for phase retrieval and compressed sensing with random generative priorscited by 20
  22. 2019Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrievalcited by 18
  23. 2020The Generalized Lasso with Nonlinear Observations and Generative Priorscited by 15
  24. 2021Provable Compressed Sensing with Generative Priors via Langevin Dynamicscited by 14
  25. 2021Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priorscited by 14
  26. 2017Structured signal recovery from quadratic measurements: Breaking sample complexity barriers via nonconvex optimizationcited by 13
  27. 2022Generative Principal Component Analysiscited by 12
  28. 2016Phase Retrieval Meets Statistical Learning Theory: A Flexible Convex Relaxationcited by 11
  29. 2021Solving phase retrieval with random initial guess is nearly as good as by spectral initializationcited by 9
  30. 2022Non-Iterative Recovery from Nonlinear Observations using Generative Modelscited by 9
  31. 2016Sparse Phase Retrieval via Truncated Amplitude Flowcited by 8
  32. 2015L1-Regularized Least Squares for Support Recovery of High Dimensional Single Index Models with Gaussian Designscited by 6
  33. 2016Fast and Reliable Parameter Estimation from Nonlinear Observationscited by 5
  34. 2022Projected Gradient Descent Algorithms for Solving Nonlinear Inverse Problems with Generative Priorscited by 5
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  36. 2015Learning Single Index Models in High Dimensionscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 3; 2026: 2.

7 papers.

  1. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  2. 2023Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priorscited by 4
  3. 2024Generalized Eigenvalue Problems with Generative Priorscited by 3
  4. 2025Learning Single Index Models with Diffusion Priorscited by 2
  5. 2026Image Restoration via Diffusion Models with Dynamic Resolutioncited by 2
  6. 2025Diffusion Model Based Signal Recovery Under 1-Bit Quantizationcited by 1
  7. 2026Tracing the Oracle: Improving Diffusion Timestep Scheduling for 3D CT Reconstructioncited by 0