pith. sign in

arxiv: 2606.24254 · v1 · pith:UVDB5OOKnew · submitted 2026-06-23 · ⚛️ physics.optics

Enhancing Speckle Metrology with Diffusion Denoising in Photon-Starved Regimes

Admir Bajraktarevic , Alexander C. Trowbridge , Saba N. Khan , Anton van den Hengel , Graham D. Bruce , Kishan Dholakia This is my paper

Pith reviewed 2026-06-25 22:48 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords speckle metrologydiffusion denoisingphoton-starved regimeswavelength sensingintegrating spherelow-signal reconstructionprecision metrology
0
0 comments X

The pith

A diffusion denoising model separates noise from speckle patterns to enable accurate femtometre-scale wavelength sensing in low-photon conditions.

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

The paper presents a denoising framework that uses diffusion models to recover the underlying speckle structure from noisy, photon-limited measurements. It employs a hybrid strategy of pre-training on synthetic data followed by fine-tuning on a small experimental dataset, allowing direct integration into existing speckle metrology workflows. When applied to wavelength sensing with an integrating sphere, the method reduces root-mean-square error by up to 72 percent and produces usable reconstructions where standard processing fails. A reader would care because many precision metrology tasks operate under constraints of low illumination power or detector sensitivity, and this approach extends their practical range without hardware changes.

Core claim

The central claim is that a diffusion-based denoiser, trained with hybrid pre-training and experimental fine-tuning, separates measurement noise from true speckle structure in low-signal data and integrates into metrology pipelines, thereby reducing root-mean-square error by up to 72 percent and enabling accurate femtometre-scale wavelength estimates with an integrating sphere where conventional speckle metrology fails.

What carries the argument

A hybrid pre-training plus small-dataset fine-tuning strategy for a diffusion model that isolates speckle structure from photon noise and plugs directly into existing metrology pipelines.

If this is right

  • The framework enables accurate speckle-based measurements under illumination powers or detector sensitivities that previously rendered the technique unusable.
  • It extends the operational range of integrating-sphere wavelength sensing to spectral regions lacking sensitive detectors.
  • The same denoising step can be inserted into other speckle metrology pipelines without redesigning the optical setup.
  • Root-mean-square error reductions of up to 72 percent are achieved specifically in the photon-starved regime.

Where Pith is reading between the lines

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

  • If the model generalizes across different speckle-generating geometries, it could reduce reliance on high-power sources in environmental sensing applications.
  • The approach might be tested on dynamic speckle patterns to see whether temporal coherence is preserved after denoising.
  • A natural extension would be to quantify how much the fine-tuning dataset size can be reduced before bias appears in the wavelength estimates.

Load-bearing premise

The hybrid pre-training plus small-dataset fine-tuning produces a model that separates measurement noise from true speckle structure without introducing systematic biases that would affect downstream metrology quantities such as wavelength estimates.

What would settle it

A side-by-side comparison in which denoised low-signal speckle patterns yield wavelength estimates with larger systematic offsets from a high-signal reference than the raw low-signal patterns would falsify the claim of unbiased separation.

read the original abstract

Laser speckle is a powerful tool for precision metrology that enables highly sensitive measurements of light sources and subtle environmental perturbations. Many applications require operation in photon-limited regimes, for example when using low-power illumination or in spectral regions where sensitive detectors are unavailable. In these conditions, the structured speckle pattern that encodes the signal becomes challenging to disentangle from measurement noise, severely degrading performance. Here, we introduce a denoising framework to separate measurement noise from the underlying speckle structure in low-signal data. Using a hybrid pre-training and experimental fine-tuning strategy, the model is adapted using a small experimental dataset and integrates directly with existing speckle metrology pipelines. Applied to femtometre-scale wavelength sensing using an integrating sphere, the approach reduces root-mean-square error in low-signal conditions by up to 72% and enables accurate reconstruction where conventional speckle metrology fails.

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 paper introduces a denoising framework based on a hybrid pre-trained diffusion model that is fine-tuned on a small experimental dataset. The model is integrated into existing speckle metrology pipelines to separate photon noise from underlying speckle structure in low-signal regimes. Applied to femtometre-scale wavelength sensing with an integrating sphere, the approach is claimed to reduce RMSE by up to 72% and enable accurate reconstruction where conventional methods fail.

Significance. If the central claim holds and the denoising step preserves wavelength-dependent speckle correlations at the required precision, the work could extend the usable range of speckle-based sensors into photon-starved conditions, with direct relevance to low-power or infrared metrology applications.

major comments (2)
  1. [Abstract] Abstract: the headline claim of up to 72% RMSE reduction and 'accurate reconstruction where conventional speckle metrology fails' rests on the unverified assumption that the diffusion model removes noise while exactly preserving speckle autocorrelation length and contrast; no quantitative comparison (e.g., autocorrelation functions or wavelength residuals against high-signal ground truth) is referenced to confirm this preservation at femtometre precision.
  2. The hybrid pre-training plus small-dataset fine-tuning strategy is presented as sufficient to avoid systematic biases in downstream metrology quantities, yet the manuscript provides no ablation or residual analysis demonstrating that high-frequency spatial features encoding the wavelength shift remain unaltered after denoising.
minor comments (1)
  1. Notation for the integrating-sphere sensor geometry and the precise definition of the femtometre-scale wavelength shift should be introduced earlier to allow readers to assess the required preservation accuracy.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The concerns regarding verification of speckle property preservation are well-taken, and we address each point below with plans for revision where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim of up to 72% RMSE reduction and 'accurate reconstruction where conventional speckle metrology fails' rests on the unverified assumption that the diffusion model removes noise while exactly preserving speckle autocorrelation length and contrast; no quantitative comparison (e.g., autocorrelation functions or wavelength residuals against high-signal ground truth) is referenced to confirm this preservation at femtometre precision.

    Authors: The reported RMSE is computed directly on the downstream wavelength estimate against high-signal ground-truth references, which quantifies preservation of the wavelength-dependent speckle information at the femtometre scale. This end-to-end metric already incorporates any degradation in autocorrelation or contrast that would affect metrology performance. Nevertheless, we agree that explicit autocorrelation-function comparisons and wavelength-residual plots would make the preservation claim more transparent and will add these figures and associated quantitative metrics to the revised manuscript. revision: yes

  2. Referee: The hybrid pre-training plus small-dataset fine-tuning strategy is presented as sufficient to avoid systematic biases in downstream metrology quantities, yet the manuscript provides no ablation or residual analysis demonstrating that high-frequency spatial features encoding the wavelength shift remain unaltered after denoising.

    Authors: The fine-tuning dataset consists of paired low- and high-signal experimental speckle patterns that already encode the same wavelength shifts, so the model is explicitly trained to recover those features. However, we did not include dedicated ablation studies isolating high-frequency content or residual maps. We will incorporate such analyses (including spatial-frequency power spectra before/after denoising and residual error maps) in the revision to directly demonstrate absence of systematic bias in the metrology-relevant features. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical performance claim with no self-referential derivation

full rationale

The paper presents an applied machine-learning denoising method whose central claims are empirical performance metrics (72% RMSE reduction on wavelength sensing) obtained from hybrid pre-training plus fine-tuning on experimental data. No equations, uniqueness theorems, or fitted parameters are shown to reduce the reported improvement to a self-definition or to a prediction that is statistically forced by the training procedure itself. The abstract and described pipeline contain no load-bearing self-citations, ansatzes smuggled via prior work, or renaming of known results; the derivation chain is therefore self-contained as a standard empirical validation of a denoising pipeline.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; assessment is therefore empty.

pith-pipeline@v0.9.1-grok · 5702 in / 991 out tokens · 23045 ms · 2026-06-25T22:48:23.526975+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

46 extracted references · 32 canonical work pages · 1 internal anchor

  1. [1]

    Nature Commu- nications8(1), 15610 (2017) https://doi.org/ 10.1038/ncomms15610

    Metzger, N.K., Spesyvtsev, R., Bruce, G.D., Miller, B., Maker, G.T., Malcolm, G., Mazilu, M., Dholakia, K.: Harnessing speckle for a sub-femtometre resolved broadband waveme- ter and laser stabilization. Nature Commu- nications8(1), 15610 (2017) https://doi.org/ 10.1038/ncomms15610

    work page doi:10.1038/ncomms15610 2017

  2. [2]

    arXiv preprint arXiv:2604.00506 (2026) https://doi.org/10

    Monteiro, G.B., Perrella, C., Scholten, S.K., Facchin, M., Luiten, A.N., Bruce, G.D., Dho- lakia, K.: Ultra-high precision speckle spec- trometer enabling radio-frequency scale res- olution of atomic spectra. arXiv preprint arXiv:2604.00506 (2026) https://doi.org/10. 48550/arXiv.2604.00506

    arXiv 2026

  3. [3]

    Scientific Reports13(1), 14607 (2023) https: //doi.org/10.1038/s41598-023-40518-6

    Facchin, M., Bruce, G.D., Dholakia, K.: Measuring picometre-level displace- ments using speckle patterns produced by an integrating sphere. Scientific Reports13(1), 14607 (2023) https: //doi.org/10.1038/s41598-023-40518-6

    work page doi:10.1038/s41598-023-40518-6 2023

  4. [4]

    Nature Reviews Physics6(8), 500–508 (2024) https://doi

    Facchin, M., Khan, S.N., Dholakia, K., Bruce, G.D.: Determining intrinsic sensi- tivity and the role of multiple scatter- ing in speckle metrology. Nature Reviews Physics6(8), 500–508 (2024) https://doi. org/10.1038/s42254-024-00735-y

    work page doi:10.1038/s42254-024-00735-y 2024

  5. [5]

    Nature Com- munications (2026) https://doi.org/10.1038/ s41467-026-72281-3

    Perrella, C., Punse, A.A., Zalogina, A., Szy- dzik, C., Lim, M., Boes, A., Mitchell, A., Dunning, K.R., Dholakia, K.: Speckle-based measurement of the fractional azimuthal index of orbital angular momentum beams for refractive index sensing. Nature Com- munications (2026) https://doi.org/10.1038/ s41467-026-72281-3

    2026

  6. [6]

    Jour- nal of Optics27(7), 075402 (2025) https: //doi.org/10.1088/2040-8986/ade8fb

    Trowbridge, A.C., Wright, E.M., Dholakia, K.: Radiation pressure revisited: historical context and the role of structured light. Jour- nal of Optics27(7), 075402 (2025) https: //doi.org/10.1088/2040-8986/ade8fb

    work page doi:10.1088/2040-8986/ade8fb 2025

  7. [7]

    Journal of Biomedi- cal Optics27(3), 030901 (2022) https://doi

    Silva, V.B., Andrade De Jesus, D., Klein, S., Walsum, T., Cardoso, J., Brea, L.S., Vaz, P.G.: Signal-carrying speckle in optical coher- ence tomography: a methodological review on biomedical applications. Journal of Biomedi- cal Optics27(3), 030901 (2022) https://doi. org/10.1117/1.JBO.27.3.030901

    work page doi:10.1117/1.jbo.27.3.030901 2022

  8. [8]

    ACS Photonics9(3), 830–836 (2022) https://doi

    Facchin, M., Bruce, G.D., Dholakia, K.: Mea- surement of variations in gas refractive index with 10–9 resolution using laser speckle. ACS Photonics9(3), 830–836 (2022) https://doi. org/10.1021/acsphotonics.1c01355

    work page doi:10.1021/acsphotonics.1c01355 2022

  9. [9]

    Journal of Physics: Photonics3(3), 035005 (2021) https: //doi.org/10.1088/2515-7647/ac107a

    Facchin, M., Dholakia, K., Bruce, G.D.: 11 Wavelength sensitivity of the speckle patterns produced by an integrating sphere. Journal of Physics: Photonics3(3), 035005 (2021) https: //doi.org/10.1088/2515-7647/ac107a

    work page doi:10.1088/2515-7647/ac107a 2021

  10. [10]

    Journal of Biomedical Optics26(9) (2021) https:// doi.org/10.1117/1.JBO.26.9.090601

    Hajjarian, Z., Nadkarni, S.K.: Technological perspectives on laser speckle micro-rheology for cancer mechanobiology research. Journal of Biomedical Optics26(9) (2021) https:// doi.org/10.1117/1.JBO.26.9.090601

    work page doi:10.1117/1.jbo.26.9.090601 2021

  11. [11]

    Journal of Biomedical Optics24(8), 080901 (2019) https://doi.org/10.1117/1.JBO.24.8

    Heeman, W., Steenbergen, W., Van Dam, G.M., Boerma, E.C.: Clinical applications of laser speckle contrast imaging: a review. Journal of Biomedical Optics24(8), 080901 (2019) https://doi.org/10.1117/1.JBO.24.8. 080901

    work page doi:10.1117/1.jbo.24.8 2019

  12. [12]

    IEEE Reviews in Biomedical Engi- neering9, 106–120 (2016) https://doi.org/10

    Vaz, P.G., Humeau-Heurtier, A., Figueiras, E., Correia, C., Cardoso, J.: Laser speckle imaging to monitor microvascular blood flow: A review. IEEE Reviews in Biomedical Engi- neering9, 106–120 (2016) https://doi.org/10. 1109/RBME.2016.2532598

    arXiv 2016

  13. [13]

    Journal of Biophoton- ics9(6), 626–636 (2016) https://doi.org/10

    Gong, P., Es’haghian, S., Harms, K.-A., Mur- ray, A., Rea, S., Kennedy, B.F., Wood, F.M., Sampson, D.D., McLaughlin, R.A.: Optical coherence tomography for longitudinal mon- itoring of vasculature in scars treated with laser fractionation. Journal of Biophoton- ics9(6), 626–636 (2016) https://doi.org/10. 1002/jbio.201500157

    2016

  14. [14]

    Biomedical Optics Express5(3), 817 (2014) https://doi.org/10.1364/BOE.5.000817

    Tripathi, M.M., Hajjarian, Z., Van Cott, E.M., Nadkarni, S.K.: Assessing blood coag- ulation status with laser speckle rheology. Biomedical Optics Express5(3), 817 (2014) https://doi.org/10.1364/BOE.5.000817

    work page doi:10.1364/boe.5.000817 2014

  15. [15]

    Journal of Biomedical Optics4(1), 95–105 (1999) https://doi.org/10.1117/1.429925

    Schmitt, J.M., Xiang, S.H., Yung, K.M.: Speckle in optical coherence tomography. Journal of Biomedical Optics4(1), 95–105 (1999) https://doi.org/10.1117/1.429925

    work page doi:10.1117/1.429925 1999

  16. [16]

    https:// doi.org/10.48550/arXiv.2510.09077

    Kumar, B., Bruce, G.D., Negro, L.D., Schulz, S.A.: Performance limit of on- chip speckle spectrometers (2025). https:// doi.org/10.48550/arXiv.2510.09077 . https:// arxiv.org/abs/2510.09077

    work page doi:10.48550/arxiv.2510.09077 2025

  17. [17]

    Optics Express30(12), 20666–20683 (2022) https: //doi.org/10.1364/OE.459213

    Fang, Q., Xia, H., Song, Q., Zhang, M., Guo, R., Montresor, S., Picart, P.: Speckle denoising based on deep learning via a conditional generative adversarial network in digital holographic interferometry. Optics Express30(12), 20666–20683 (2022) https: //doi.org/10.1364/OE.459213

    work page doi:10.1364/oe.459213 2022

  18. [19]

    Computers in Biology and Medicine152, 106474 (2023) https://doi.org/10.1016/j.compbiomed.2022

    Goceri, E.: Evaluation of denoising tech- niques to remove speckle and Gaussian noise from dermoscopy images. Computers in Biology and Medicine152, 106474 (2023) https://doi.org/10.1016/j.compbiomed.2022. 106474

    work page doi:10.1016/j.compbiomed.2022 2023

  19. [20]

    Computer Methods and Pro- grams in Biomedicine274, 109150 (2024) https://doi.org/10.1016/j.cmpb.2025.109150

    Sivaanpu, A., Punithakumar, K., Zheng, R., Nguyen, K.-C.T., Noga, M., Ta, D., Lou, E.H.M., Le, L.H.: Speckle noise reduction techniques in ultrasound imaging: A com- prehensive review of the last two decades (2005–2024). Computer Methods and Pro- grams in Biomedicine274, 109150 (2024) https://doi.org/10.1016/j.cmpb.2025.109150

    work page doi:10.1016/j.cmpb.2025.109150 2005

  20. [21]

    Denoising Diffusion Probabilistic Models

    Ho, J., Jain, A., Abbeel, P.: Denoising Diffu- sion Probabilistic Models (2020). https://doi. org/10.48550/arXiv.2006.11239

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2006.11239 2020

  21. [22]

    In: Bach, F., Blei, D

    Sohl-Dickstein, J., Weiss, E., Mah- eswaranathan, N., Ganguli, S.: Deep unsupervised learning using nonequilibrium thermodynamics. In: Bach, F., Blei, D. (eds.) Proceedings of the 32nd International Con- ference on Machine Learning. Proceedings of Machine Learning Research, vol. 37, pp. 2256–2265. PMLR, Lille, France (2015)

    2015

  22. [23]

    In: Meila, M., Zhang, T

    Nichol, A.Q., Dhariwal, P.: Improved denois- ing diffusion probabilistic models. In: Meila, M., Zhang, T. (eds.) Proceedings of the 38th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 139, pp. 8162–8171. PMLR, Virtual Event (2021)

    2021

  23. [24]

    Journal of Electronic Imag- ing33(4), 043003 (2024) https://doi.org/10

    Yang, C., Wang, C., Liang, L., Su, Z.: 12 Real-world image denoising via efficient diffusion model with controllable noise generation. Journal of Electronic Imag- ing33(4), 043003 (2024) https://doi.org/10. 1117/1.JEI.33.4.043003

    2024

  24. [25]

    Journal of Physics: Photonics7(1), 013001 (2025) https://doi.org/10.1088/2515-7647/ada101

    Bachimanchi, H., Volpe, G.: Dif- fusion models for super-resolution microscopy: a tutorial. Journal of Physics: Photonics7(1), 013001 (2025) https://doi.org/10.1088/2515-7647/ada101

    work page doi:10.1088/2515-7647/ada101 2025

  25. [26]

    Com- munications Engineering3(1), 186 (2024) https://doi.org/10.1038/s44172-024-00331-z

    Li, R., Della Maggiora, G., Andriasyan, V., Petkidis, A., Yushkevich, A., Deshpande, N., Kudryashev, M., Yakimovich, A.: Microscopy image reconstruction with physics-informed denoising diffusion probabilistic model. Com- munications Engineering3(1), 186 (2024) https://doi.org/10.1038/s44172-024-00331-z

    work page doi:10.1038/s44172-024-00331-z 2024

  26. [27]

    IEEE Transactions on Pattern Analysis and Machine Intelligence15(2), 1233–1252 (2024) https://doi.org/10.1364/BOE.515520

    He, C., Shen, Y., Fang, C., Xiao, F., Tang, L., Zhang, Y., Zuo, W., Guo, Z., Li, X.: Dif- fusion models in low-level vision: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence15(2), 1233–1252 (2024) https://doi.org/10.1364/BOE.515520

    work page doi:10.1364/boe.515520 2024

  27. [28]

    Kok, Y.E., Bentley, A., Parkes, A.J., Somekh, M.G., Wright, A.J., Pound, M.P.: Practi- cal aberration correction using deep transfer learning with limited experimental data. Opt. Express33(6), 14431–14444 (2025) https:// doi.org/10.1364/OE.557993

    work page doi:10.1364/oe.557993 2025

  28. [29]

    APL Photonics10(3), 031102 (2025) https://doi

    Peterkovic, Z., Upadhya, A., Perrella, C., Bajraktarevic, A., Bautista Gonzalez, R.E., Lim, M., Dunning, K.R., Dholakia, K.: Opti- mizing image capture for low-light widefield quantitative fluorescence microscopy. APL Photonics10(3), 031102 (2025) https://doi. org/10.1063/5.0245239

    work page doi:10.1063/5.0245239 2025

  29. [30]

    Optics Express20(23), 25970 (2012) https://doi

    Pret, A.V., Gronheid, R., Engelen, J., Yan, P.-Y., Leeson, M.J., Younkin, T.R.: Evidence of speckle in extreme-UV lithography. Optics Express20(23), 25970 (2012) https://doi. org/10.1364/OE.20.025970

    work page doi:10.1364/oe.20.025970 2012

  30. [31]

    Journal of Biomed- ical Optics25(5), 050801 (2020) https://doi

    Hajjarian, Z., Nadkarni, S.K.: Tutorial on laser speckle rheology: technology, applica- tions, and opportunities. Journal of Biomed- ical Optics25(5), 050801 (2020) https://doi. org/10.1117/1.JBO.25.5.050801

    work page doi:10.1117/1.jbo.25.5.050801 2020

  31. [32]

    Physics-Informed Machine Learning

    Karniadakis, G.E., Kevrekidis, I.G., Lu, L., Perdikaris, P., Wang, S., Yang, L.: Physics- informed machine learning. Nature Reviews Physics3(6), 422–440 (2021) https://doi. org/10.1038/s42254-021-00314-5

    work page doi:10.1038/s42254-021-00314-5 2021

  32. [33]

    In: Medical Image Com- puting and Computer-Assisted Intervention – MICCAI 2024 vol

    Tivnan, M., Yoon, S., Chen, Z., Li, X., Wu, D., Li, Q.: Hallucination index: An image quality metric for generative recon- struction models. In: Medical Image Com- puting and Computer-Assisted Intervention – MICCAI 2024 vol. 15010, pp. 449–458. Springer, Cham (2024). https://doi.org/10. 1007/978-3-031-72117-5 42

    2024

  33. [34]

    In: Proceedings of the 2015 ACM/SIGDA International Sym- posium on Field-programmable Gate Arrays, pp

    Zhang, C., Li, P., Sun, G., Guan, Y., Xiao, B., Cong, J.: Optimizing FPGA- based accelerator design for deep convolu- tional neural networks. In: Proceedings of the 2015 ACM/SIGDA International Sym- posium on Field-programmable Gate Arrays, pp. 161–170 (2015). https://doi.org/10.1145/ 2684746.2689060

    arXiv 2015

  34. [35]

    IEEE Transac- tions on Computer-Aided Design of Inte- grated Circuits and Systems36(3), 513–517 (2016) https://doi.org/10.1109/TCAD.2016

    Wang, C., Gong, L., Yu, Q., Li, X., Xie, Y., Zhou, X.: Dlau: A scalable deep learning accelerator unit on FPGA. IEEE Transac- tions on Computer-Aided Design of Inte- grated Circuits and Systems36(3), 513–517 (2016) https://doi.org/10.1109/TCAD.2016. 2587683

    work page doi:10.1109/tcad.2016 2016

  35. [36]

    emnlp-main.1332/

    Shawahna, A., Sait, S.M., El-Maleh, A.: FPGA-based accelerators of deep learning networks for learning and classification: A review. IEEE Access7, 7823–7859 (2018) https://doi.org/10.1109/ACCESS.2018. 2890150

    work page doi:10.1109/access.2018 2018

  36. [37]

    GitHub (2022)

    Platen, P., Patil, S., Lozhkov, A., Cuenca, P., Lambert, N., Rasul, K., Davaadorj, M., Nair, D., Paul, S., Berman, W., Xu, Y., Liu, S., Wolf, T.: Diffusers: State-of-the-art diffusion models. GitHub (2022)

    2022

  37. [38]

    U-net: Convolutional networks for biomedical image segmentation, in: Navab, N., Hornegger, J., III, W.M.W., Frangi, A.F

    Ronneberger, O., Fischer, P., Brox, T.: U- net: Convolutional networks for biomedical image segmentation. In: Navab, N., Horneg- ger, J., Wells, W.M., Frangi, A.F. (eds.) 13 Medical Image Computing and Computer- Assisted Intervention – MICCAI 2015, pp. 234–241. Springer, Cham (2015). https://doi. org/10.1007/978-3-319-24574-4 28

    work page doi:10.1007/978-3-319-24574-4 2015

  38. [39]

    SPIE Press, Bellingham, WA, USA (2024)

    Goodman, J.W.: Simulating Speckle with Python. SPIE Press, Bellingham, WA, USA (2024). Chap. 4

    2024

  39. [40]

    Journal of Machine Learning Research15(56), 1929–1958 (2014)

    Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research15(56), 1929–1958 (2014)

    1929

  40. [41]

    Medical & Biological Engi- neering & Computing50(6), 547–558 (2012) https://doi.org/10.1007/s11517-012-0902-z

    Basak, K., Manjunatha, M., Dutta, P.K.: Review of laser speckle-based analysis in medical imaging. Medical & Biological Engi- neering & Computing50(6), 547–558 (2012) https://doi.org/10.1007/s11517-012-0902-z

    work page doi:10.1007/s11517-012-0902-z 2012

  41. [42]

    OSA Continuum3(5), 1302 (2020) https:// doi.org/10.1364/OSAC.394117

    Facchin, M., Bruce, G.D., Dholakia, K.: Speckle-based determination of the polarisa- tion state of single and multiple laser beams. OSA Continuum3(5), 1302 (2020) https:// doi.org/10.1364/OSAC.394117

    work page doi:10.1364/osac.394117 2020

  42. [43]

    Physical Review X7(4), 041053 (2017) https: //doi.org/10.1103/PhysRevX.7.041053

    Ambichl, P., Xiong, W., Bromberg, Y., Red- ding, B., Cao, H., Rotter, S.: Super- and anti- principal-modes in multimode waveguides. Physical Review X7(4), 041053 (2017) https: //doi.org/10.1103/PhysRevX.7.041053

    work page doi:10.1103/physrevx.7.041053 2017

  43. [44]

    Nature Photonics9(11), 751–757 (2015) https://doi.org/10.1038/nphoton.2015.188

    Carpenter, J., Eggleton, B.J., Schr¨ oder, J.: Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre. Nature Photonics9(11), 751–757 (2015) https://doi.org/10.1038/nphoton.2015.188

    work page doi:10.1038/nphoton.2015.188 2015

  44. [45]

    on lines and planes of closest fit to systems of points in space

    Pearson, K.: Liii. on lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin philo- sophical magazine and journal of science 2(11), 559–572 (1901) https://doi.org/10. 1080/14786440109462720

    1901

  45. [46]

    Optics Letters44(6), 1367 (2019) https://doi.org/10.1364/OL.44

    Bruce, G.D., O’Donnell, L., Chen, M., Dho- lakia, K.: Overcoming the speckle correla- tion limit to achieve a fiber wavemeter with attometer resolution. Optics Letters44(6), 1367 (2019) https://doi.org/10.1364/OL.44. 001367

    work page doi:10.1364/ol.44 2019

  46. [47]

    Journal of Machine Learning Research12, 2825–2830 (2011) 14

    Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, E.: Scikit-learn: Machine learning in Python. Journal of Machine Learning Research12, 2825–2830 (2011) 14

    2011