mlsanityData to 7 Oct 2026

QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Models

arXiv 2302.00919 ↗First posted 2 Feb 2023eess.SP cs.IT cs.LGcited by 4

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

In practical compressed sensing (CS), the obtained measurements typically necessitate quantization to a limited number of bits prior to transmission or storage. This nonlinear quantization process poses significant recovery challenges, particularly with extreme coarse quantization such as 1-bit. Recently, an efficient algorithm called QCS-SGM was proposed for quantized CS (QCS) which utilizes score-based generative models (SGM) as an implicit prior. Due to the adeptness of SGM in capturing the intricate structures of natural signals, QCS-SGM substantially outperforms previous QCS methods. However, QCS-SGM is constrained to (approximately) row-orthogonal sensing matrices as the computation of the likelihood score becomes intractable otherwise. To address this limitation, we introduce an advanced variant of QCS-SGM, termed QCS-SGM+, capable of handling general matrices effectively. The key idea is a Bayesian inference perspective on the likelihood score computation, wherein expectation propagation is employed for its approximate computation. Extensive experiments are conducted, demonstrating the substantial superiority of QCS-SGM+ over QCS-SGM for general sensing matrices beyond mere row-orthogonality.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 23 of its 51 references that are in the map. First posted on arXiv 2 Feb 2023.

Builds on

23 of 51 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022Quantized Compressed Sensing with Score-based Generative Models2 Nov
  2. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Probabilistic Models19 Jun
  5. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 18

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  6. 2017Compressed Sensing using Generative Modelscited by 337
  7. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  8. 2020Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulationcited by 225
  9. 2013Expectation Propagation for approximate Bayesian inferencecited by 172
  10. 2019Invertible generative models for inverse problems: mitigating representation error and dataset biascited by 93
  11. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 58
  12. 2020Approximate Message Passing algorithms for rotationally invariant matricescited by 31
6 more
  1. 2020Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priorscited by 21
  2. 2021Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passingcited by 18
  3. 2019Global Guarantees for Blind Demodulation with Generative Priorscited by 11
  4. 2022Non-Iterative Recovery from Nonlinear Observations using Generative Modelscited by 9
  5. 2020Semi-analytic approximate stability selection for correlated data in generalized linear modelscited by 2
  6. 2022A Unitary Transform Based Generalized Approximate Message Passingcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025Generative Spectrum Cartography: Unified Reconstruction and Active Sensing via Diffusion Modelscited by 1
  2. 2025Score-Based Turbo Message Passing for Plug-and-Play Compressive Imagingcited by 0
  3. 2026Deep Probabilistic Unfolding for Quantized Compressive Sensingcited by 0
  4. 2026Posterior Information Dynamics of Diffusion Models for Linear Inverse Problemscited by 0

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