pith. sign in

arxiv: 2606.29849 · v1 · pith:G3OD6XE3new · submitted 2026-06-29 · ⚛️ physics.optics

Hessian sparsity-constrained self-supervised network for near-infrared single-photon single-pixel imaging

Yao Wang , Muchen Zhu , Linjun Zhai , Huiyuan Zhang , Junnan Chen , Yiming Yu , Zhaohua Yang , Baolei Liu
show 1 more author
Fan Wang
This is my paper

Pith reviewed 2026-06-30 05:32 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords near-infrared imagingsingle-pixel imagingsingle-photon detectionself-supervised networkHessian constraintsparsity regularizationlow-light imagingnoise suppression
0
0 comments X

The pith

An untrained neural network constrained by sparsity and Hessian structure reconstructs high-fidelity near-infrared single-pixel images down to 0.01 photons per pixel.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces HS3N, which folds the physical forward model of single-pixel imaging into an untrained network. Sparsity priors and Hessian-based terms regularize the network to remove photon noise while keeping structural continuity. This combination is tested in both simulations and laboratory experiments on near-infrared scenes. A sympathetic reader would see value in reaching usable images where photon counts are so low that conventional detectors or algorithms produce unusable results. The work also shows the method running at video rates on moving objects under low flux.

Core claim

The central claim is that an untrained network regularized by sparsity priors together with Hessian-based structural constraints, when combined with the physical forward model of single-pixel imaging, suppresses noise sufficiently to produce high-fidelity near-infrared reconstructions at photon levels as low as 0.01 per pixel, as verified in both simulation and experiment including real-time droplet monitoring at 20 Hz under 0.19 photons per pixel.

What carries the argument

The Hessian sparsity-constrained self-supervised network (HS3N), which embeds the single-pixel imaging forward model inside an untrained network and adds regularization terms that enforce sparsity and Hessian-derived structural continuity.

If this is right

  • High-fidelity reconstructions become possible under illumination levels where photon noise previously dominated.
  • Dynamic processes can be tracked at roughly 20 frames per second when flux is around 0.19 photons per pixel.
  • The same reconstruction framework applies to visible, mid-infrared, or terahertz single-pixel imaging by changing only the forward model.
  • Practical near-infrared inspection becomes feasible in extreme low-light settings without array detectors.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may lower hardware cost for low-light imaging by replacing detector arrays with a single-element sensor plus computation.
  • Similar untrained-network regularization could be tested on other photon-starved modalities such as fluorescence microscopy or quantum imaging.
  • If the Hessian constraint proves too rigid for certain textures, replacing it with learned structural priors might extend the usable range.
  • Real-time deployment would require checking how the method scales when the measurement matrix changes rapidly between frames.

Load-bearing premise

The untrained network, when regularized only by sparsity and Hessian constraints, will suppress photon noise on real experimental data without creating artifacts or needing extra tuning.

What would settle it

An experiment at 0.01 photons per pixel in which the reconstructed images show clear structural artifacts or loss of known features relative to a higher-photon reference image would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2606.29849 by Baolei Liu, Fan Wang, Huiyuan Zhang, Junnan Chen, Linjun Zhai, Muchen Zhu, Yao Wang, Yiming Yu, Zhaohua Yang.

Figure 4
Figure 4. Figure 4: Experimental results with infrared-absorbing targets. (a) Photograph of the experimental target, a coverslip with a randomly distributed infrared-absorbing spot (cyan circle). (b) Reconstructed images of the target in (a) using three different reconstruction algorithms, DGI, GIDC and HS3N. (c) Photograph of a syringe needle tip without an infrared￾absorbing droplet. (d) Reconstructed images of the needle t… view at source ↗
read the original abstract

Near-infrared (NIR) imaging has emerged as an important technology for night vision, remote sensing, and biological imaging, yet conventional array-detector-based systems are often limited by insufficient sensitivity, high cost, and substantial dark noise. Single-pixel imaging (SPI) offers an attractive alternative, enabling single-photon-level NIR imaging by using a cost-effective single-element detector. Nevertheless, SPI remains restricted by photon noise, leading to degraded imaging quality and limited frame rate under extremely low photon flux conditions. Here, we present a Hessian sparsity-constrained self-supervised network (HS3N) for single-photon NIR SPI, which can suppress noise and enable high-fidelity and real-time imaging under ultra-low illumination conditions. The HS3N integrates the physical forward model of SPI with an untrained neural network regularized by both sparsity priors and Hessian-based structural constraints, enabling effective noise suppression while preserving structural fidelity and continuity. Both simulated and experimental results demonstrate that HS3N enables high-fidelity reconstructions under ultra-low NIR photon levels down to ~0.01 photons per pixel. Furthermore, we demonstrate its dynamic capability by monitoring the dynamic evolution and detachment of infrared-absorbing droplets, at a frame rate of ~20 Hz under ~0.19 photons per pixel, highlighting its potential for high-sensitivity infrared inspection. The proposed reconstruction framework paves the way for practical NIR imaging in extreme low light conditions, which can be extended to visible, mid-infrared or terahertz imaging, offering broad potential for photon-efficient sensing across a wide spectral range.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a Hessian sparsity-constrained self-supervised network (HS3N) for near-infrared single-photon single-pixel imaging. It integrates the physical forward model of SPI with an untrained neural network regularized by sparsity priors and Hessian-based structural constraints to suppress photon noise while preserving structural fidelity. Both simulated and experimental results are presented to support high-fidelity reconstructions at ultra-low photon levels down to ~0.01 photons per pixel, with an additional demonstration of dynamic imaging at ~20 Hz under ~0.19 photons per pixel.

Significance. If the central performance claims hold under rigorous validation, the work would be significant for advancing practical, cost-effective NIR imaging in extreme low-light regimes relevant to night vision, remote sensing, and biological applications. The self-supervised formulation that embeds the physical forward model directly into the reconstruction, combined with untrained-network regularization, is a methodological strength that avoids the need for large labeled datasets and may generalize across spectral ranges.

major comments (2)
  1. [Abstract/Results] Abstract and Results sections: the claim of high-fidelity reconstruction at ~0.01 photons per pixel is presented without reported error bars, statistical analysis across multiple trials, quantitative baseline comparisons (e.g., to total-variation or other sparsity-based methods), or ablation studies isolating the contribution of the Hessian term versus the sparsity prior. These omissions make the central performance claim difficult to verify and undermine assessment of robustness against photon noise.
  2. [Methods/Results] Methods/Results: the regularization weights for the sparsity and Hessian terms are not described with a selection procedure or sensitivity analysis; without this, it is unclear whether the reported performance requires post-hoc tuning on the evaluation data, which would weaken the claim that the untrained network reliably suppresses noise without introducing artifacts.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'high-fidelity' is used without specifying the quantitative metrics (PSNR, SSIM, or structural similarity indices) or the ground-truth references employed in the simulated and experimental evaluations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight opportunities to strengthen the statistical rigor and methodological transparency of the manuscript. We address each major comment below and have prepared revisions to incorporate the requested elements.

read point-by-point responses

  1. Referee: [Abstract/Results] Abstract and Results sections: the claim of high-fidelity reconstruction at ~0.01 photons per pixel is presented without reported error bars, statistical analysis across multiple trials, quantitative baseline comparisons (e.g., to total-variation or other sparsity-based methods), or ablation studies isolating the contribution of the Hessian term versus the sparsity prior. These omissions make the central performance claim difficult to verify and undermine assessment of robustness against photon noise.

    Authors: We agree that the current presentation would benefit from expanded quantitative validation. The revised manuscript will add error bars derived from multiple independent trials, statistical analysis (including mean and standard deviation metrics), direct quantitative comparisons against total-variation and other sparsity-based baselines, and ablation studies that isolate the Hessian term's contribution relative to the sparsity prior alone. revision: yes

  2. Referee: [Methods/Results] Methods/Results: the regularization weights for the sparsity and Hessian terms are not described with a selection procedure or sensitivity analysis; without this, it is unclear whether the reported performance requires post-hoc tuning on the evaluation data, which would weaken the claim that the untrained network reliably suppresses noise without introducing artifacts.

    Authors: We will revise the Methods section to explicitly describe the regularization weight selection procedure (including any heuristic or validation-based approach employed) and include a sensitivity analysis demonstrating how reconstruction quality varies with these parameters, thereby clarifying that the reported performance does not rely on post-hoc tuning specific to the test data. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper describes a self-supervised reconstruction method that integrates the known SPI physical forward model with an untrained network subject to explicit sparsity and Hessian structural priors. Performance is asserted via separate simulated and experimental test cases at low photon flux, not via any equation that re-derives the output metric from the same fitted quantities used for evaluation. No self-citation chain, ansatz smuggling, or renaming of known results is invoked as load-bearing support for the central claim. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of the physical forward model of single-pixel imaging and the effectiveness of the chosen regularizers; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption The physical forward model of SPI accurately describes the measurement process under the stated low-photon conditions.
    Invoked when the network is integrated with the physical model.
  • domain assumption Sparsity priors and Hessian-based structural constraints are appropriate regularizers for preserving image fidelity in NIR single-photon data.
    Used to regularize the untrained network.

pith-pipeline@v0.9.1-grok · 5832 in / 1429 out tokens · 29008 ms · 2026-06-30T05:32:50.114602+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

30 extracted references

  1. [1]

    Heat -assisted detection and ranging,

    F. Bao, X. Wang, S. H. Sureshbabu, G. Sreekumar, L. Yang, V. Aggarwal, V. N. Boddeti, and Z. Jacob, "Heat -assisted detection and ranging," Nature 619(7971), 743– 748 (2023)

    2023

  2. [2]

    Near -infrared luminescence high -contrast in vivo biomedical imaging,

    Y. Chen, S. Wang, and F. Zhang, "Near -infrared luminescence high -contrast in vivo biomedical imaging," Nat. Rev. Bioeng. 1(1), 60–78 (2023)

    2023

  3. [3]

    Advanced fluorescence imaging technology in the near-infrared-II window for biomedical applications,

    C. Li, G. Chen, Y. Zhang, F. Wu, and Q. Wang, "Advanced fluorescence imaging technology in the near-infrared-II window for biomedical applications," J. Am. Chem. Soc. 142(35), 14789–14804 (2020)

    2020

  4. [4]

    Controllable surface-grafted MXene inks for electromagnetic wave modulation and infrared anti - counterfeiting applications,

    Z. Deng, L. Li, P. Tang, C. Jiao, Z. Z. Yu, C. M. Koo, and H. Bin Zhang, "Controllable surface-grafted MXene inks for electromagnetic wave modulation and infrared anti - counterfeiting applications," ACS Nano 16(10), 16976–16986 (2022)

    2022

  5. [5]

    Room temperature operation of germanium – silicon single-photon avalanche diode,

    N. Na, Y. Lu, Y. Liu, P. Chen, Y. Lai, Y. Lin, C. Lin, T. Shia, C. Cheng, and S. Chen, "Room temperature operation of germanium – silicon single-photon avalanche diode," Nature 627(8003), 295–300 (2024)

    2024

  6. [6]

    Video -Rate Infrared Focal Plane Array Based on Solution-Processed Black Phosphorus Films,

    S. Bianconi, V. K. Sangwan, S. V. Rangnekar, J. Rabinowitz, C. M. Kang, L. M. Guiney, M. C. Hersam, and H. Mohseni, "Video -Rate Infrared Focal Plane Array Based on Solution-Processed Black Phosphorus Films," ACS Photonics 12(3), 1507–1514 (2025)

    2025

  7. [7]

    Infrared -to-visible upconversion devices,

    T. Rao, M. Chen, G. Mu, and X. Tang, "Infrared -to-visible upconversion devices," Coatings 12(4), 456 (2022)

    2022

  8. [8]

    Principles and prospects for single-pixel imaging,

    M. P. Edgar, G. M. Gibson, and M. J. Padgett, "Principles and prospects for single-pixel imaging," Nat. Photonics 13(1), 13–20 (2019)

    2019

  9. [9]

    Self -evolving ghost imaging,

    B. Liu, F. Wang, C. Chen, F. Dong, and D. McGloin, "Self -evolving ghost imaging," Optica 8(10), 1340–1349 (2021)

    2021

  10. [10]

    Differential ghost imaging,

    F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, "Differential ghost imaging," Phys. Rev. Lett. 104(25), 253603 (2010)

    2010

  11. [11]

    Experimental comparison of single-pixel imaging algorithms,

    L. Bian, J. Suo, Q. Dai, and F. Chen, "Experimental comparison of single-pixel imaging algorithms," J. Opt. Soc. Am. A 35(1), 78–87 (2018)

    2018

  12. [12]

    Single-pixel imaging via compressive sampling,

    M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, "Single-pixel imaging via compressive sampling," IEEE Signal Process. Mag. 25(2), 83–91 (2008)

    2008

  13. [13]

    Compressive ghost imaging,

    O. Katz, Y. Bromberg, and Y. Silberberg, "Compressive ghost imaging," Appl. Phys. Lett. 95(13), 93–96 (2009)

    2009

  14. [14]

    Deep learning for real-time single-pixel video,

    C. F. Higham, R. Murray -Smith, M. J. Padgett, and M. P. Edgar, "Deep learning for real-time single-pixel video," Sci. Rep. 8(1), 2369 (2018)

    2018

  15. [15]

    Far-field super- resolution ghost imaging with a deep neural network constraint,

    F. Wang, C. Wang, M. Chen, W. Gong, Y. Zhang, S. Han, and G. Situ, "Far-field super- resolution ghost imaging with a deep neural network constraint," Light Sci. Appl. 11(1), 1–11 (2022)

    2022

  16. [16]

    Robust single -photon single -pixel imaging with self -supervised deep learning,

    K. Song, H. Liu, Y. Bian, D. Wang, L. Han, R. Li, S. Zhao, F. Zhang, H. Ge, S. Han, and L. Xiao, "Robust single -photon single -pixel imaging with self -supervised deep learning," Opt. Laser Technol. 197(79), 114749 (2026)

    2026

  17. [17]

    Computational and dark -field ghost imaging with ultraviolet light,

    J. Song, B. Liu, Y. Wang, C. Chen, X. Shan, X. Zhong, L. -A. Wu, and F. Wang, "Computational and dark -field ghost imaging with ultraviolet light," Photonics Res. 12(2), 226–234 (2024)

    2024

  18. [18]

    Dual -mode adaptive-SVD ghost imaging,

    D. Wang, B. Liu, J. Song, Y. Wang, X. Shan, X. Zhong, and F. Wang, "Dual -mode adaptive-SVD ghost imaging," Opt. Express 31(9), 14225–14239 (2023)

    2023

  19. [19]

    Time -Resolved Nonlinear Ghost Imaging,

    L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, "Time -Resolved Nonlinear Ghost Imaging," ACS Photonics 5(8), 3379–3388 (2018)

    2018

  20. [20]

    Physics-informed neural network enhanced multispectral single -pixel imaging with a chip spectral detector,

    M. Zhu, B. Liu, Y. Wang, L. Zhai, J. Song, N. Liu, Z. Yang, L. Ding, and F. Wang, "Physics-informed neural network enhanced multispectral single -pixel imaging with a chip spectral detector," Opt. Laser Technol. 194, 114430 (2026)

    2026

  21. [21]

    Photon -counting single-pixel camera based on a fast spinning coding disk,

    Z. Zhao, Y. Zhang, J. Song, M. -F. Li, and L. -A. Wu, "Photon -counting single-pixel camera based on a fast spinning coding disk," Opt. Lett. 50(1), 169–172 (2025)

    2025

  22. [22]

    Full-color photon -counting single -pixel imaging,

    Y.-N. Zhao, H.-Y. Hou, J.-C. Han, H.-C. Liu, S.-H. Zhang, D.-Z. Cao, and B.-L. Liang, "Full-color photon -counting single -pixel imaging," Opt. Lett. 46(19), 4900 –4903 (2021)

    2021

  23. [23]

    High -quality photon -limited imaging through dynamic and complex scattering media with a single -photon detector,

    Y. Hao, Y. Peng, T. Zhang, and W. Chen, "High -quality photon -limited imaging through dynamic and complex scattering media with a single -photon detector," APL Photonics 10(10), 106119 (2025)

    2025

  24. [24]

    Imaging with a small number of photons,

    P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, "Imaging with a small number of photons," Nat. Commun. 6(1), 5913 (2015)

    2015

  25. [25]

    Short -wave infrared compressive imaging of single photons,

    T. Gerrits, D. J. Lum, V. Verma, J. Howell, R. P. Mirin, and S. W. Nam, "Short -wave infrared compressive imaging of single photons," Opt. Express 26(12), 15519 (2018)

    2018

  26. [26]

    Deep learning optimized single-pixel LiDAR,

    N. Radwell, S. D. Johnson, M. P. Edgar, C. F. Higham, R. Murray -Smith, and M. J. Padgett, "Deep learning optimized single-pixel LiDAR," Appl. Phys. Lett. 115, 231101 (2019)

    2019

  27. [27]

    Mid -infrared single-pixel imaging at the single-photon level,

    Y. Wang, K. Huang, J. Fang, M. Yan, E. Wu, and H. Zeng, "Mid -infrared single-pixel imaging at the single-photon level," Nat. Commun. 14(1), 1073 (2023)

    2023

  28. [28]

    Dual -wavelength 3D single- pixel imaging based on gated photon counting,

    J. Liu, Z. Yang, Y. Tian, Z. Zhao, Z. Dong, and B. Liu, "Dual -wavelength 3D single- pixel imaging based on gated photon counting," Opt. Lasers Eng. 195, 109269 (2025)

    2025

  29. [29]

    Spa rse deconvolution improves the resolution of live -cell super -resolution fluorescence microscopy,

    W. Zhao, S. Zhao, L. Li, X. Huang, S. Xing, Y. Zhang, G. Qiu, Z. Han, Y. Shang, D. en Sun, C. Shan, R. Wu, L. Gu, S. Zhang, R. Chen, J. Xiao, Y. Mo, J. Wang, W. Ji, X. Chen, B. Ding, Y. Liu, H. Mao, B. L. Song, J. Tan, J. Liu, H. Li, and L. Chen, "Spa rse deconvolution improves the resolution of live -cell super -resolution fluorescence microscopy," Nat. ...

    2022

  30. [30]

    Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,

    X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, "Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy," Nat. Biotechnol. 36(5), 451–459 (2018)

    2018