mlsanityData to 7 Oct 2026

Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors

arXiv 2108.03570 ↗First posted 8 Aug 2021cs.LG cs.IT math.ITcited by 7

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Abstract (arXiv)

In 1-bit compressive sensing, each measurement is quantized to a single bit, namely the sign of a linear function of an unknown vector, and the goal is to accurately recover the vector. While it is most popular to assume a standard Gaussian sensing matrix for 1-bit compressive sensing, using structured sensing matrices such as partial Gaussian circulant matrices is of significant practical importance due to their faster matrix operations. In this paper, we provide recovery guarantees for a correlation-based optimization algorithm for robust 1-bit compressive sensing with randomly signed partial Gaussian circulant matrices and generative models. Under suitable assumptions, we match guarantees that were previously only known to hold for i.i.d.~Gaussian matrices that require significantly more computation. We make use of a practical iterative algorithm, and perform numerical experiments on image datasets to corroborate our theoretical results.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 21 of its 64 references that are in the map. First posted on arXiv 8 Aug 2021.

Builds on

21 of 64 references.

References · 21

  1. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  2. 2017Compressed Sensing using Generative Modelscited by 337
  3. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  4. 2018Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networkscited by 120
  5. 2018Phase Retrieval Under a Generative Priorcited by 73
  6. 2021Intermediate Layer Optimization for Inverse Problems using Deep Generative Modelscited by 70
  7. 2018Compressed Sensing with Deep Image Prior and Learned Regularizationcited by 47
  8. 2020Robust Compressed Sensing using Generative Modelscited by 33
  9. 2019An Introductory Guide to Fano's Inequality with Applications in Statistical Estimationcited by 30
  10. 2019Information-Theoretic Lower Bounds for Compressive Sensing with Generative Modelscited by 25
  11. 2020Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priorscited by 21
  12. 2020The Generalized Lasso with Nonlinear Observations and Generative Priorscited by 15
9 more
  1. 2021Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priorscited by 14
  2. 2019Global Guarantees for Blind Demodulation with Generative Priorscited by 11
  3. 2014One-bit compressive sensing with norm estimationcited by 10
  4. 2019Robust One-Bit Recovery via ReLU Generative Networks: Near-Optimal Statistical Rate and Global Landscape Analysiscited by 8
  5. 2015Binary Embedding: Fundamental Limits and Fast Algorithmcited by 5
  6. 2015On Binary Embedding using Circulant Matricescited by 4
  7. 2016Near-Optimal Sample Complexity Bounds for Circulant Binary Embeddingcited by 3
  8. 2018Robust one-bit compressed sensing with partial circulant matricescited by 3
  9. 2016Fast binary embeddings with Gaussian circulant matrices: improved boundscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 0; 2024: 0; 2025: 3; 2026: 1.

7 papers.

  1. 2022Generative Principal Component Analysiscited by 12
  2. 2022Non-Iterative Recovery from Nonlinear Observations using Generative Modelscited by 9
  3. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  4. 2022Projected Gradient Descent Algorithms for Solving Nonlinear Inverse Problems with Generative Priorscited by 5
  5. 2025Learning Single Index Models with Diffusion Priorscited by 2
  6. 2026Image Restoration via Diffusion Models with Dynamic Resolutioncited by 2
  7. 2025One-bit Compressed Sensing using Generative Modelscited by 1