mlsanityData to 14 Oct 2026

Non-Iterative Recovery from Nonlinear Observations using Generative Models

arXiv 2205.15749 ↗First posted 31 May 2022cs.LG cs.CVcited by 9

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Abstract (arXiv)

In this paper, we aim to estimate the direction of an underlying signal from its nonlinear observations following the semi-parametric single index model (SIM). Unlike conventional compressed sensing where the signal is assumed to be sparse, we assume that the signal lies in the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. This is mainly motivated by the tremendous success of deep generative models in various real applications. Our reconstruction method is non-iterative (though approximating the projection step may use an iterative procedure) and highly efficient, and it is shown to attain the near-optimal statistical rate of order √(k log L)/m, where m is the number of measurements. We consider two specific instances of the SIM, namely noisy 1-bit and cubic measurement models, and perform experiments on image datasets to demonstrate the efficacy of our method. In particular, for the noisy 1-bit measurement model, we show that our non-iterative method significantly outperforms a state-of-the-art iterative method in terms of both accuracy and efficiency.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 33 of its 71 references that are in the map. First posted on arXiv 31 May 2022.

Builds on

33 of 71 references.

References · 33

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21 more
  1. 2018Phase Retrieval Under a Generative Priorcited by 73
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Cited by year

Citing papers per year: 2022: 4; 2023: 4; 2024: 0; 2025: 1.

9 papers.

  1. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  2. 2022Quantized Compressed Sensing with Score-based Generative Modelscited by 15
  3. 2023CS4ML: A general framework for active learning with arbitrary data based on Christoffel functionscited by 11
  4. 2022A coherence parameter characterizing generative compressed sensing with Fourier measurementscited by 8
  5. 2022Misspecified Phase Retrieval with Generative Priorscited by 7
  6. 2023A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensingcited by 7
  7. 2023QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Modelscited by 4
  8. 2023Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priorscited by 4
  9. 2025Learning Single Index Models with Diffusion Priorscited by 2