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arxiv: 2605.22197 · v1 · pith:2JOLVVEQnew · submitted 2026-05-21 · ⚛️ physics.optics

A Residual-Subspace Constraint Framework for Fourier Ptychographic Microscopy

Sui-peng Wang , Si-yi Xie , Chang-tao Cai , Zhun Wei , Rui Chen This is my paper

Pith reviewed 2026-05-22 03:45 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords Fourier ptychographic microscopyresidual subspace constraintmodel-reality gapphase retrievalcomputational imagingoptical aberrationsrobust reconstructionsubspace decomposition
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The pith

Embedding a residual-subspace constraint into the iterative engine enables high-fidelity Fourier ptychographic microscopy without hardware calibration.

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

The paper introduces a Residual-Subspace Constraint Framework (RSCF) for Fourier ptychographic microscopy to handle the model-reality gap. It decomposes residuals into low-rank systematic mismatches and stochastic noise to isolate stable information manifolds that do not depend on exact forward-model accuracy. These manifolds are then embedded as constraints inside the reconstruction iterations. The result is selective suppression of error-amplifying components, yielding better phase and amplitude recovery. A sympathetic reader would care because the method promises robust performance under aberrations and misalignments without exhaustive calibration steps.

Core claim

The central claim is that residuals between the idealized forward model and the physical imaging process can be decomposed via subspace methods into a low-rank systematic component that remains invariant to forward-model inaccuracies together with stochastic noise; embedding the resulting subspace constraint into the iterative engine selectively suppresses error-amplifying components and thereby achieves high-fidelity phase and amplitude recovery without explicit hardware calibration.

What carries the argument

The Residual-Subspace Constraint Framework (RSCF), which applies subspace decomposition to residuals to isolate invariant low-rank manifolds and incorporates them as constraints within the iterative reconstruction process.

Load-bearing premise

Residuals between the idealized forward model and the physical imaging process can be decomposed into a low-rank systematic component that remains invariant to forward-model inaccuracies plus stochastic noise.

What would settle it

A controlled test in which the low-rank residual subspace extracted from one forward-model perturbation is applied to data generated under a different perturbation and the reconstruction fidelity drops below that of an un-constrained baseline method.

Figures

Figures reproduced from arXiv: 2605.22197 by Chang-tao Cai, Rui Chen, Si-yi Xie, Sui-peng Wang, Zhun Wei.

Figure 1
Figure 1. Figure 1: RSCF reconstruction workflow. Consisting of six steps: 1) generate low [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Full-FOV high resolution reconstruction of a plant stem cross-section. (a) [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 讨论：低 质量数据 的重建 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Ideal LED position Shifted y (mm) x (mm) (b) Object Spectrum LED misalignment (c) Aberration mPIE AS-FPM FD-FPM Proposed FD-FPM Proposed 16 18 20 22 PSNRmPIE AS-FPM 15 16 FD-FPM Proposed 0.30 0.35 0.40 SSIM mPIE AS-FPM 0.2 0.3 (a) -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Ideal LED position Shifted y (mm) x (mm) 1.2 0 0 1 a.u. 0 2 4 6 8 10 [P… view at source ↗
Figure 5
Figure 5. Figure 5: 讨论3： 实验数据 的不用k 重建结果 比较 (a) 100% (c) (b) 90% 80% 95% 85% 70% 实验数据：分辨率靶 Fig5_UASF1951- 20260127-90th 【20260127finish】 Figure5_different_k Led_num=15*15 H = 92 * 1000 D = 4 * 1000 Lambda = 0.632 R_overlap = 0.7883 90th (d) 0 10 20 30 40 50 60 70 80 90 100 0.0 0.5 1.0 Amplitude Pixels 70% 80% 85% 90% 95% 100% FD-FPM 400μm [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of reconstruction results under different principal component [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Full-FOV reconstruction of the USAF1951 resolution target and blood smear [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: 讨论：实验 数据的分辨 率 Proposed FD-FPM Raw 10μm (c) 200μm (e) Line 𝒍𝟏 (g1) Raw 𝒍2 (j) Line 𝒍𝟐 𝒍2 10μm Proposed FD-FPM -𝜋 𝜋 𝒍𝟏 𝒍𝟏 0 10 20 30 40 50 60 70 80 90 100 0.0 0.5 1.0 Amplitude Pixels FD-FPM Proposed 0 10 20 30 40 50 60 -1.0 -0.5 0.0 0.5 Phase(rad) Pixels FD-FPM Proposed FD-FPM Proposed Raw (g) 200μm (a) (b) (c1) FD-FPM (c2) Proposed (d) (f) (g2) FD-FPM (g3) Proposed [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
read the original abstract

The reconstruction fidelity of computational optical imaging is fundamentally constrained by the model-reality gap, i.e., the inevitable discrepancy between idealized forward models and the physical imaging process. Conventional paradigms attempt to bridge this gap through exhaustive system calibration or explicit parameter estimation, which are often computationally intensive and prone to severe non-convex stagnation. This paper introduces a Residual-Subspace Constraint Framework (RSCF) to achieve robust Fourier ptychographic microscopy. Instead of treating residuals as unstructured errors, RSCF leverages subspace decomposition to decouple low-rank, systematic mismatches from stochastic noise, thereby isolating stable information manifolds that remain invariant to forward-model inaccuracies. By embedding this subspace constraint into the iterative engine, the framework selectively suppresses error-amplifying components, enabling high-fidelity phase and amplitude recovery without explicit hardware calibration. Numerical simulations and experimental validations demonstrate that RSCF yields superior convergence acceleration and artifact suppression under severe optical aberrations and LED misalignment. This information-centric paradigm provides a versatile, model-agnostic strategy to enhance robustness across diverse computational imaging modalities.

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

1 major / 2 minor

Summary. The manuscript introduces a Residual-Subspace Constraint Framework (RSCF) for Fourier ptychographic microscopy to address the model-reality gap. It decomposes residuals into a low-rank systematic component and stochastic noise, then embeds a subspace constraint on the low-rank part into the iterative reconstruction to suppress error-amplifying components. This is claimed to enable high-fidelity phase and amplitude recovery without explicit hardware calibration. Numerical simulations and experiments are said to show superior convergence acceleration and artifact suppression under severe optical aberrations and LED misalignment.

Significance. If the invariance of the extracted low-rank residual subspace to forward-model inaccuracies can be established, the framework would offer a model-agnostic approach to improving robustness in computational imaging modalities, potentially reducing the computational burden and non-convexity issues associated with explicit calibration or parameter estimation.

major comments (1)
  1. Abstract and §3: The central claim that the low-rank residual subspace 'remains invariant to forward-model inaccuracies' is asserted without derivation or test. No analysis shows why the principal components of residuals r_low are unchanged when the forward operator H is replaced by a perturbed Ĥ (e.g., unknown LED angles or aberrations). This invariance is load-bearing for the 'without explicit hardware calibration' claim; if the low-rank directions shift with model error, the constraint risks projecting away signal rather than artifacts.
minor comments (2)
  1. Abstract: While superior convergence and artifact suppression are claimed, no quantitative metrics (e.g., iteration counts, RMSE reductions, or comparison tables) are provided to support the assertions.
  2. §3: The residual decomposition r = r_low + r_noise and the precise form of the subspace constraint should be stated with explicit equations rather than descriptive text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive critique. The concern regarding the invariance of the low-rank residual subspace is well-taken and central to the framework's claims. We address it directly below and are prepared to strengthen the manuscript accordingly.

read point-by-point responses

  1. Referee: Abstract and §3: The central claim that the low-rank residual subspace 'remains invariant to forward-model inaccuracies' is asserted without derivation or test. No analysis shows why the principal components of residuals r_low are unchanged when the forward operator H is replaced by a perturbed Ĥ (e.g., unknown LED angles or aberrations). This invariance is load-bearing for the 'without explicit hardware calibration' claim; if the low-rank directions shift with model error, the constraint risks projecting away signal rather than artifacts.

    Authors: We agree that a formal justification of the invariance is necessary to support the model-agnostic claim. The manuscript motivates the property by noting that systematic residuals from model mismatches (aberrations, LED position errors) are low-rank and arise from a limited set of physical mechanisms, while stochastic noise is unstructured. Empirical support is provided via simulations that introduce controlled perturbations to the forward model and demonstrate that RSCF still recovers high-fidelity reconstructions; however, we did not include an explicit derivation or quantitative subspace-overlap analysis. In the revised version we will add a short theoretical subsection in §3 that derives the approximate invariance under bounded perturbations ΔH (showing that the dominant left singular vectors of the residual matrix remain stable when the perturbation lies in a low-dimensional operator space). We will also augment the numerical section with a new figure reporting the principal-angle distance between subspaces extracted under nominal and perturbed models across a range of aberration and misalignment strengths. These additions will clarify the conditions under which the constraint suppresses artifacts rather than signal. revision: yes

Circularity Check

0 steps flagged

No significant circularity; subspace constraint introduced as independent modeling choice

full rationale

The paper presents RSCF as a new framework that applies subspace decomposition to residuals to isolate low-rank components claimed to be invariant to forward-model inaccuracies. No equations or steps are shown that define the subspace constraint in terms of the recovered phase/amplitude or fit it to the target result by construction. The invariance is asserted as a leveraged property of the decomposition rather than derived from the reconstruction output itself. No self-citation load-bearing steps, fitted inputs renamed as predictions, or ansatz smuggling appear in the provided claims. The derivation chain is self-contained, with the constraint serving as an added modeling assumption to suppress artifacts.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that imaging residuals admit a useful low-rank plus noise decomposition; no free parameters or new entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Residuals between idealized forward model and physical process admit decomposition into low-rank systematic mismatches and stochastic noise.
    Invoked to justify subspace constraint that isolates invariant information manifolds.

pith-pipeline@v0.9.0 · 5717 in / 1142 out tokens · 35774 ms · 2026-05-22T03:45:40.611791+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages · 2 internal anchors

  1. [1]

    Computational imaging,

    J. N. Mait, G. W. Euliss, and R. A. Athale, “Computational imaging,” Adv. Opt. Photon.10, 409–483 (2018)

    work page 2018

  2. [2]

    Future-proof imaging: computational imaging,

    J. Liu, Y. Feng, Y. Wang,et al., “Future-proof imaging: computational imaging,” Adv. Imaging1, 012001 (2024)

    work page 2024

  3. [3]

    Physicaltwinningforjointencoding-decodingoptimizationincomputationaloptics: a review,

    L.Bian, X.Zhan, R.Yan,et al., “Physicaltwinningforjointencoding-decodingoptimizationincomputationaloptics: a review,” Light. Sci. & Appl.14, 162 (2025)

    work page 2025

  4. [4]

    Computational optical imaging: on the convergence of physical and digital layers,

    Z. Wang, Y. Peng, L. Fang, and L. Gao, “Computational optical imaging: on the convergence of physical and digital layers,” Optica12, 113–130 (2025)

    work page 2025

  5. [5]

    A survey on super-resolution imaging,

    J. Tian and K.-K. Ma, “A survey on super-resolution imaging,” Signal, Image Video Process.5, 329–342 (2011)

    work page 2011

  6. [6]

    Wide-field,high-resolutionfourierptychographicmicroscopy,

    G.Zheng,R.Horstmeyer,andC.Yang,“Wide-field,high-resolutionfourierptychographicmicroscopy,”Nat.Photonic 7, 739–745 (2013)

    work page 2013

  7. [7]

    End-to-end optimization of optics and image processing for achromatic extended depth of field and super-resolution imaging,

    V. Sitzmann, S. Diamond, Y. Peng,et al., “End-to-end optimization of optics and image processing for achromatic extended depth of field and super-resolution imaging,” ACM Trans. Graph.37, 114 (2018)

    work page 2018

  8. [8]

    Quantitative phase imaging: Recent advances and expanding potential in biomedicine,

    T. L. Nguyen, S. Pradeep, R. L. Judson-Torres,et al., “Quantitative phase imaging: Recent advances and expanding potential in biomedicine,” ACS Nano16, 11516–11544 (2022)

    work page 2022

  9. [9]

    Learning to see in the dark,

    C. Chen, Q. Chen, J. Xu, and V. Koltun, “Learning to see in the dark,” inProceedings of the IEEE conference on computer vision and pattern recognition,(2018), pp. 3291–3300

    work page 2018

  10. [10]

    Computational optical imaging: An overview,

    C. Zuo and Q. Chen, “Computational optical imaging: An overview,” Infrared Laser Eng.51, 158–341 (2022)

    work page 2022

  11. [11]

    Vignetting effect in fourier ptychographic microscopy,

    A. Pan, Chao Zuo, Yuege Xie,et al., “Vignetting effect in fourier ptychographic microscopy,” Opt. Lasers Eng.120, 40–48 (2019)

    work page 2019

  12. [12]

    Image reconstruction with imperfect forward models and applications in deblurring,

    Y. Korolev and J. Lellmann, “Image reconstruction with imperfect forward models and applications in deblurring,” SIAM J. on Imaging Sci.11, 197–218 (2018)

    work page 2018

  13. [13]

    Differentiable imaging: A new tool for computational optical imaging,

    N. Chen, L. Cao, T.-C. Poon,et al., “Differentiable imaging: A new tool for computational optical imaging,” Adv. Phys. Res.2, 2200118 (2023)

    work page 2023

  14. [14]

    Non-convex optimization for inverse problem solving in computer-generated holography,

    X. Sui, Z. He, D. Chu, and L. Cao, “Non-convex optimization for inverse problem solving in computer-generated holography,” Light. Sci. & Appl.13, 158 (2024)

    work page 2024

  15. [15]

    Differentiable imaging: Progress, challenges, and outlook,

    N. Chen, D. J. Brady, and E. Y. Lam, “Differentiable imaging: Progress, challenges, and outlook,” Adv. Devices & Instrum.6, 0117 (2025)

    work page 2025

  16. [16]

    A differentiable wave optics model for end-to-end computational imaging system optimization,

    C.-J. Ho, Y. Belhe, S. Rotenberg,et al., “A differentiable wave optics model for end-to-end computational imaging system optimization,” in2025 IEEE/CVF International Conference on Computer Vision (ICCV),(2025), pp. 28042–28051

    work page 2025

  17. [17]

    Uncertainty-aware Fourier ptychography,

    N. Chen, Y. Wu, C. Tan,et al., “Uncertainty-aware Fourier ptychography,” Light. Sci. & Appl.14, 236 (2025)

    work page 2025

  18. [18]

    Fourier ptychographic microscopy with untrained deep neural network priors,

    Q. Chen, D. Huang, and R. Chen, “Fourier ptychographic microscopy with untrained deep neural network priors,” Opt. Express30, 39597–39612 (2022)

    work page 2022

  19. [19]

    Concept, implementations and applications of fourier ptychography,

    G. Zheng, C. Shen, S. Jiang,et al., “Concept, implementations and applications of fourier ptychography,” Nat. Rev. Phys.3, 207–223 (2021)

    work page 2021

  20. [20]

    Anisotropic regularization for sparsely sampled and noise-robust fourier ptychography,

    K. C. Lee, H. Chae, S. Xu,et al., “Anisotropic regularization for sparsely sampled and noise-robust fourier ptychography,” Opt. Express32, 25343–25361 (2024)

    work page 2024

  21. [21]

    Under-sampling reconstruction with total variational optimization for fourier ptychographic microscopy,

    Q. Shi, W. Hui, K. Huang,et al., “Under-sampling reconstruction with total variational optimization for fourier ptychographic microscopy,” Opt. Commun.492, 126986 (2021)

    work page 2021

  22. [22]

    LED-based temporal variant noise model for fourier ptychographic microscopy,

    Q. Ma, J. Zhao, and G. Cui, “LED-based temporal variant noise model for fourier ptychographic microscopy,” Opt. Express32, 14620–14644 (2024)

    work page 2024

  23. [23]

    Digital aberration correction for enhanced thick tissue imaging exploiting aberration matrix and tilt-tilt correlation from the optical memory effect,

    C. Oh, H. Hugonnet, M. Lee, and Y. Park, “Digital aberration correction for enhanced thick tissue imaging exploiting aberration matrix and tilt-tilt correlation from the optical memory effect,” Nat. Commun.16, 1685 (2025)

    work page 2025

  24. [24]

    Tolerance-aware deep optics,

    J. Dai, L. Chen, X. Yang,et al., “Tolerance-aware deep optics,” arXiv, arXiv:2502.04719 (2025)

    work page arXiv 2025

  25. [25]

    Computational adaptive optics for high-resolution non-line-of-sight imaging,

    Z. Ou, J. Wu, Y. Yang, and X. Zheng, “Computational adaptive optics for high-resolution non-line-of-sight imaging,” Opt. Express30, 4583–4591 (2022)

    work page 2022

  26. [26]

    Model adaptation for inverse problems in imaging,

    D. Gilton, G. Ongie, and R. Willett, “Model adaptation for inverse problems in imaging,” IEEE Trans. on Comput. Imaging7, 661–674 (2021)

    work page 2021

  27. [27]

    Plug-and-play priors for model based reconstruction,

    S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-play priors for model based reconstruction,” in 2013 IEEE Global Conference on Signal and Information Processing,(2013), pp. 945–948

    work page 2013

  28. [28]

    Physics-guided deep learning for color fourier ptychographic microscopy under low-frequency spectrum acquisition,

    Y. He, R. Zhao, S.-P. Wang,et al., “Physics-guided deep learning for color fourier ptychographic microscopy under low-frequency spectrum acquisition,” Appl. Opt.65, 3356–3365 (2026)

    work page 2026

  29. [29]

    On the use of deep learning for computational imaging,

    G. Barbastathis, A. Ozcan, and G. Situ, “On the use of deep learning for computational imaging,” Optica6, 921–943 (2019)

    work page 2019

  30. [30]

    Fourier ptychographic microscopy with a two-stage physics-enhanced neural network,

    Q. Chen, C.-T. Cai, X.-T. He, and R. Chen, “Fourier ptychographic microscopy with a two-stage physics-enhanced neural network,” Opt. & Laser Technol.181, 112016 (2025)

    work page 2025

  31. [31]

    System calibration method for fourier ptychographic microscopy,

    A. Pan, Y. Zhang, T. Zhao,et al., “System calibration method for fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017)

    work page 2017

  32. [32]

    FPM-WSI: Fourier ptychographic whole slide imaging via feature-domain backdiffraction,

    S. Zhang, A. Wang, J. Xu,et al., “FPM-WSI: Fourier ptychographic whole slide imaging via feature-domain backdiffraction,” Optica11, 634–646 (2024)

    work page 2024

  33. [33]

    Wavelet-Forward Family Enabling Stitching-Free Full-Field Fourier Ptychographic Microscopy,

    H. Wu, J. Wang, H. Pan,et al., “Wavelet-Forward Family Enabling Stitching-Free Full-Field Fourier Ptychographic Microscopy,” Laser & Photonics Rev.19, 2401183 (2025)

    work page 2025

  34. [34]

    High-Fidelity Computational Microscopy via Feature-Domain Phase Retrieval,

    S. Zhang, A. Pan, H. Sun,et al., “High-Fidelity Computational Microscopy via Feature-Domain Phase Retrieval,” Adv. Sci.12, 2413975 (2025)

    work page 2025

  35. [35]

    Fourier ptychographic microscopy 10 years on: a review,

    F. Xu, Z. Wu, C. Tan,et al., “Fourier ptychographic microscopy 10 years on: a review,” Cells13, 324 (2024)

    work page 2024

  36. [36]

    Efficientpositionalmisalignmentcorrectionmethodforfourierptychographic microscopy,

    J.Sun,Q.Chen,Y.Zhang,andC.Zuo,“Efficientpositionalmisalignmentcorrectionmethodforfourierptychographic microscopy,” Biomed. Opt. Express7, 1336–1350 (2016)

    work page 2016

  37. [37]

    Embedded pupil function recovery for fourier ptychographic microscopy,

    X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for fourier ptychographic microscopy,” Opt. Express22, 4960–4972 (2014)

    work page 2014

  38. [38]

    Quantitative phase imaging based on holography: trends and new perspectives,

    Z. Huang and L. Cao, “Quantitative phase imaging based on holography: trends and new perspectives,” Light. Sci. & Appl.13, 145 (2024)

    work page 2024

  39. [39]

    Ptychographic x-ray computed tomography at the nanoscale,

    M. Dierolf, A. Menzel, P. Thibault,et al., “Ptychographic x-ray computed tomography at the nanoscale,” Nature467, 436–439 (2010)

    work page 2010

  40. [40]

    Experimental robustness of fourier ptychography phase retrieval algorithms,

    L.-H. Yeh, J. Dong, J. Zhong,et al., “Experimental robustness of fourier ptychography phase retrieval algorithms,” Opt. Express23, 33214–33240 (2015)

    work page 2015

  41. [41]

    J. W. Goodman,Introduction to Fourier Optics(Macmillan Learning, 2017), 4th ed

    work page 2017

  42. [42]

    Principal component analysis: a review and recent developments,

    I. T. Jolliffe and J. Cadima, “Principal component analysis: a review and recent developments,” Philos. transactions royal society A: Math. Phys. Eng. Sci.374, 20150202 (2016)

    work page 2016

  43. [43]

    On the early history of the singular value decomposition,

    G. W. Stewart, “On the early history of the singular value decomposition,” SIAM Rev.35, 551–566 (1993)

    work page 1993

  44. [44]

    Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions,

    N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions,” SIAM Rev.53, 217–288 (2011)

    work page 2011

  45. [45]

    An overview of gradient descent optimization algorithms

    S. Ruder, “An overview of gradient descent optimization algorithms,” arXiv, arXiv:1609.04747 (2016)

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  46. [46]

    Prior-free depth-of-field extension capability of fourier ptychographic microscopy via various optimizers,

    Y. Liao, J. Xu, T. Feng,et al., “Prior-free depth-of-field extension capability of fourier ptychographic microscopy via various optimizers,” Appl. Opt.64, 5121–5128 (2025)

    work page 2025

  47. [47]

    Spatial-and fourier-domain ptychography for high-throughput bio-imaging,

    S. Jiang, P. Song, T. Wang,et al., “Spatial-and fourier-domain ptychography for high-throughput bio-imaging,” Nat. protocols18, 2051–2083 (2023)

    work page 2051

  48. [48]

    Further improvements to theptychographical iterative engine,

    A. Maiden, D.Johnson, andP. Li, “Further improvements to theptychographical iterative engine,” Optica4, 736–745 (2017)

    work page 2017

  49. [49]

    Adaptive step-size strategy for noise-robust fourier ptychographic microscopy,

    C. Zuo, J. Sun, and Q. Chen, “Adaptive step-size strategy for noise-robust fourier ptychographic microscopy,” Opt. Express24, 20724–20744 (2016)

    work page 2016

  50. [50]

    Revisiting Small Batch Training for Deep Neural Networks

    D. Masters and C. Luschi, “Revisiting small batch training for deep neural networks,” arXiv, arXiv:1804.07612 (2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018