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arxiv: 2605.04186 · v1 · submitted 2026-05-05 · ⚛️ physics.flu-dyn

Recognition: 3 theorem links

· Lean Theorem

Real-Time Estimation of High-Resolution Flow Fields and Reduced-Order Coordinates from Event-Based Imaging Velocimetry

L. Franceschelli , E. Amico , C.E. Willert , M. Raiola , G. Cafiero , S. Discetti
Authors on Pith no claims yet

Pith reviewed 2026-05-08 18:03 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords event-based imaging velocimetryhigh-resolution velocity reconstructionreduced-order modelingKalman filteringPOD latent spaceturbulent flow estimationreal-time flow diagnostics
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The pith

A data-driven method uses offline POD models and online Kalman filtering to turn coarse real-time event-based velocity snapshots into high-resolution flow fields that stay dynamically consistent.

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

The paper develops a framework that first extracts low-resolution velocity snapshots from event-based imaging velocimetry in real time. Offline paired low- and high-resolution data are used to build a mapping through a POD basis together with a linear dynamical model in the resulting latent space. Online, each new low-resolution snapshot is projected, its corresponding high-resolution coordinates are estimated and smoothed by one of three estimators, and the full field is reconstructed from the retained modes. Tests on a submerged jet and a ribbed channel flow show that the approach recovers instantaneous states, turbulent kinetic energy, spectra, and temporal coherence more reliably than cubic interpolation of the low-resolution data alone. Most of the computational cost remains in the initial low-resolution processing, so the added refinement step supports higher update rates without sacrificing dynamical fidelity.

Core claim

By learning an LR-to-HR mapping and a linear dynamical model in a POD-based latent space from offline paired data, then applying estimators such as a direct Kalman filter, a linear stochastic estimator with Kalman filtering, or its variance-rescaled variant, each incoming low-resolution rt-EBIV snapshot can be projected, its high-resolution coordinates estimated and temporally regularized, and the full high-resolution velocity field reconstructed from the retained POD modes.

What carries the argument

A POD-based latent space equipped with an offline-fitted linear dynamical model that performs online temporal regularization and high-resolution coordinate estimation before reconstruction.

If this is right

  • High-resolution instantaneous flow states and turbulent kinetic energy become recoverable from deliberately coarse real-time processing.
  • Spectra and reduced-order dynamics remain more temporally coherent than those obtained by simple interpolation.
  • Real-time operation can extend to higher update rates because the dominant cost stays in low-resolution event analysis.
  • The reconstructed fields support observer-based flow-control applications that rely on consistent latent coordinates.

Where Pith is reading between the lines

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

  • The same offline-to-online split could be applied to other sparse or low-resolution imaging techniques that produce velocity snapshots.
  • Because the latent-coordinate step is cheap, the method could be paired with predictive control loops that use the estimated coordinates as state feedback.
  • If the linear model assumption holds only inside limited Reynolds-number ranges, retraining the POD basis and dynamics on a broader data set would be a direct next test.
  • The variance-rescaling variant suggests that adjusting fluctuation amplitudes after estimation may be useful for preserving higher-order statistics in other reduced-order reconstruction tasks.

Load-bearing premise

The linear dynamical model fitted in the POD latent space from offline paired data stays accurate enough for online regularization across the turbulent regimes encountered in operation.

What would settle it

Repeating the jet or channel experiments with a new turbulent case outside the training set and finding that any of the three estimators produces larger errors in spectral content or fluctuation energy than direct cubic interpolation of the low-resolution fields.

read the original abstract

We propose a data-driven framework to estimate high-resolution (HR) velocity fields and reduced-order flow coordinates from real-time Event-Based Imaging Velocimetry (rt-EBIV). Fast event analysis first provides low-resolution (LR) velocity snapshots on a coarse grid. Offline, paired LR/HR fields are used to identify the LR-to-HR mapping and a linear dynamical model in a POD-based latent space. Online, each LR snapshot is projected onto the LR basis, the corresponding HR coordinates are estimated and temporally regularized, and the HR field is reconstructed from the retained POD modes. Three estimators are compared: a direct Kalman filter (KF), a linear stochastic estimator followed by Kalman filtering (LSE), and a variance-rescaled variant (LSE+VR). The method is tested on two turbulent flows acquired with pulsed EBIV: a submerged water jet and a channel flow over a square rib. All estimators outperform direct cubic interpolation of the LR fields, yielding more consistent HR reconstructions of instantaneous flow states, turbulent kinetic energy, spectra, reduced-order dynamics, and temporal coherence. LSE gives the lowest overall reconstruction error, while LSE+VR achieves similar errors with improved recovery of fluctuation energy and higher-order content. The direct KF is the most computationally efficient and provides the closest agreement with the HR reference in spectral analyses. Since most of the cost is associated with full-field HR reconstruction, the latent-coordinate estimation is negligible compared with LR processing. The framework allows deliberately coarse rt-EBIV processing to be combined with reduced-order refinement, extending real-time operation toward higher update rates while preserving richer and dynamically consistent HR flow representations for diagnostics and future observer-based flow-control applications.

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 / 2 minor

Summary. The paper proposes a data-driven framework for real-time high-resolution (HR) velocity field and reduced-order coordinate estimation from low-resolution (LR) event-based imaging velocimetry (EBIV) snapshots. Offline paired LR/HR data are used to learn an LR-to-HR mapping and a linear dynamical model in POD latent space; online, each LR snapshot is projected and regularized via one of three estimators (direct Kalman filter, linear stochastic estimator, or variance-rescaled LSE) before POD reconstruction. The approach is demonstrated on pulsed-EBIV data from a turbulent submerged water jet and a square-rib channel flow, with all estimators reported to outperform direct cubic interpolation of the LR fields on instantaneous states, turbulent kinetic energy, spectra, reduced-order dynamics, and temporal coherence.

Significance. If the linear dynamical model in POD space is shown to be sufficiently accurate, the framework would enable deliberately coarse real-time EBIV processing while recovering dynamically consistent HR fields, which is relevant for experimental diagnostics and observer-based flow control. The work is strengthened by testing on two distinct turbulent regimes, explicit comparison of three estimators with different accuracy/complexity trade-offs, and evaluation across multiple diagnostics (instantaneous fields, TKE, spectra, coherence).

major comments (2)
  1. [Offline identification of linear dynamical model] Offline training procedure: no one-step or multi-step prediction residuals, eigenvalue spectra, or cross-validation errors are reported for the fitted linear state-space model (A, B matrices) on held-out snapshots from either the jet or rib-channel flow. This is load-bearing for the central claim, because the online estimators (KF, LSE, LSE+VR) rely on this model for temporal regularization; without demonstrated fidelity, consistent superiority over non-dynamic cubic interpolation of LR fields cannot be substantiated.
  2. [POD-based latent space and validation] Methods and results: exact POD truncation criteria (energy threshold, number of retained modes, or cross-validation procedure) and associated truncation errors are not stated, nor are quantitative error bars or statistical tests provided for the reported reconstruction errors, TKE, or spectral comparisons. These omissions weaken the support for the claim of consistent outperformance across the two flows and multiple diagnostics.
minor comments (2)
  1. [Computational considerations] The statement that 'latent-coordinate estimation is negligible compared with LR processing' would be strengthened by explicit wall-clock timings or flop counts for each estimator relative to the EBIV processing step.
  2. [Estimator definitions] Notation for the variance-rescaling factor in LSE+VR and the precise definition of the LR-to-HR mapping operator should be clarified to avoid ambiguity when reproducing the estimators.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the work's significance. We address each major comment below and outline the revisions that will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Offline identification of linear dynamical model] Offline training procedure: no one-step or multi-step prediction residuals, eigenvalue spectra, or cross-validation errors are reported for the fitted linear state-space model (A, B matrices) on held-out snapshots from either the jet or rib-channel flow. This is load-bearing for the central claim, because the online estimators (KF, LSE, LSE+VR) rely on this model for temporal regularization; without demonstrated fidelity, consistent superiority over non-dynamic cubic interpolation of LR fields cannot be substantiated.

    Authors: We agree that explicit validation metrics for the identified linear dynamical model would strengthen the presentation. Although the consistent outperformance of the dynamic estimators (KF, LSE, LSE+VR) over non-dynamic cubic interpolation—across instantaneous states, TKE, spectra, reduced-order dynamics, and temporal coherence—provides indirect evidence of model fidelity in the online regime, we will add the requested diagnostics in revision. Specifically, we will report one-step and multi-step prediction residuals on held-out data, the eigenvalue spectrum of A (to confirm stability), and any cross-validation errors for both flows. These will be included in a dedicated subsection on offline model identification. revision: yes

  2. Referee: [POD-based latent space and validation] Methods and results: exact POD truncation criteria (energy threshold, number of retained modes, or cross-validation procedure) and associated truncation errors are not stated, nor are quantitative error bars or statistical tests provided for the reported reconstruction errors, TKE, or spectral comparisons. These omissions weaken the support for the claim of consistent outperformance across the two flows and multiple diagnostics.

    Authors: We thank the referee for noting these gaps in detail. In the revised manuscript we will explicitly state the POD truncation criteria (energy threshold and number of retained modes) for each flow, report the associated truncation errors on the HR fields, and include quantitative error bars (standard deviations across independent time windows or realizations) together with statistical tests (e.g., paired comparisons) for the reconstruction errors, TKE, and spectral metrics. These additions will be placed in the Methods and Results sections to make the quantitative support for outperformance fully transparent. revision: yes

Circularity Check

0 steps flagged

No circularity: offline fitting separated from online estimation and empirical benchmarks

full rationale

The paper's chain fits an LR-to-HR mapping and linear dynamical model in POD latent space on offline paired data, then applies three estimators (KF, LSE, LSE+VR) to project and regularize online LR snapshots before reconstructing HR fields. Performance claims rest on direct comparison to HR reference data and to a non-fitted cubic interpolation baseline across two turbulent flows. No equation reduces the reported improvements in TKE, spectra, or coherence to the fitted parameters by construction; the outperformance is an external empirical result. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on data-driven fitting of an LR-to-HR mapping and a linear dynamical model from paired snapshots; these introduce free parameters whose values are chosen to match the training data rather than derived from first principles.

free parameters (2)
  • Number of retained POD modes
    Truncation level for the latent-space reconstruction; chosen to balance accuracy and cost but not derived from the equations.
  • Kalman filter tuning parameters
    Process and measurement noise covariances plus any variance-rescaling factor; fitted or hand-tuned on the offline data.
axioms (1)
  • domain assumption Flow evolution in the POD latent space can be adequately captured by a linear dynamical model.
    Invoked to enable the online temporal regularization step and the LSE/KF estimators.

pith-pipeline@v0.9.0 · 5632 in / 1423 out tokens · 59004 ms · 2026-05-08T18:03:13.338863+00:00 · methodology

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Works this paper leans on

49 extracted references · 44 canonical work pages

  1. [6]

    and Gharib, M

    Willert, Christian and Munson, M. and Gharib, M. , year =. Real-. 15th

  2. [20]

    Journal of Visualization , author =

    Real-time planar flow velocity measurements using an optical flow algorithm implemented on. Journal of Visualization , author =. 2015 , keywords =. doi:10.1007/s12650-014-0222-5 , language =

    work page doi:10.1007/s12650-014-0222-5 2015

  3. [22]

    arXiv.org , author =

    High. arXiv.org , author =

  4. [28]

    Welch, Greg and Bishop, Gary , year =. An

  5. [47]

    , Cavalieri , A.V.G

    barticle Audiffred , D.B.S. , Cavalieri , A.V.G. , Maia , I.A. , Martini , E. , Jordan , P. : Reactive experimental control of turbulent jets . Journal of Fluid Mechanics 994 , 15 ( 2024 ) 10.1017/jfm.2024.569 barticle

    work page doi:10.1017/jfm.2024.569 2024

  6. [48]

    , Zannone , M

    barticle Amico , E. , Zannone , M. , Torta , E. , Mastronuzzi , G. , Pecchio , D. , Gallo , D. , Serpieri , J. , Cafiero , G. , Morbiducci , U. : Event-based versus particle image velocimetry for cardiac flow analysis in a left-heart simulator . Physics of Fluids 38 ( 2 ), 021916 ( 2026 ) 10.1063/5.0315234 barticle

    work page doi:10.1063/5.0315234 2026

  7. [49]

    , Foxman , S.H

    barticle Bollt , S.A. , Foxman , S.H. , Gharib , M. : RapidPIV : Full Flow - Field kHz PIV for Real - Time Display and Control . arXiv preprint arXiv:2504.17987 ( 2025 ) 10.48550/arXiv.2504.17987 barticle

    work page doi:10.48550/arxiv.2504.17987 2025

  8. [50]

    , Holmes , P

    barticle Berkooz , G. , Holmes , P. , Lumley , J. : The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows . Annual Review of Fluid Mechanics 25 , 539 -- 575 ( 2003 ) 10.1146/annurev.fl.25.010193.002543 barticle

    work page doi:10.1146/annurev.fl.25.010193.002543 2003

  9. [51]

    , Vlachos , P.P

    barticle Brindise , M.C. , Vlachos , P.P. : Proper orthogonal decomposition truncation method for data denoising and order reduction . Experiments in Fluids 58 ( 4 ), 28 ( 2017 ) 10.1007/s00348-017-2320-3 barticle

    work page doi:10.1007/s00348-017-2320-3 2017

  10. [52]

    , Sanmiguel Vila , C

    barticle Cortina-Fernandez , J. , Sanmiguel Vila , C. , Ianiro , A. , Discetti , S. : From sparse data to high-resolution fields: ensemble particle modes as a basis for high-resolution flow characterization . Experimental Thermal and Fluid Science 120 , 110178 ( 2021 ) 10.1016/j.expthermflusci.2020.110178 barticle

    work page doi:10.1016/j.expthermflusci.2020.110178 2021

  11. [53]

    , Bellani , G

    barticle Discetti , S. , Bellani , G. , Orlu , R. , Serpieri , J. , Sanmiguel Vila , C. , Raiola , M. , Zheng , X. , Mascotelli , L. , Talamelli , A. , Ianiro , A. : Characterization of very-large-scale motions in high- Re pipe flows . Experimental Thermal and Fluid Science 104 , 1 -- 8 ( 2019 ) 10.1016/j.expthermflusci.2019.02.001 barticle

    work page doi:10.1016/j.expthermflusci.2019.02.001 2019

  12. [54]

    , He , C

    barticle Deng , Z.. , He , C.. , Liu , Y.. , Kim , K.C.. : Super-resolution reconstruction of turbulent velocity fields using a generative adversarial network-based artificial intelligence framework . Physics of Fluids 31 ( 12 ), 125111 ( 2019 ) 10.1063/1.5127031 barticle

    work page doi:10.1063/1.5127031 2019

  13. [55]

    , Lichtsteiner , P

    barticle Drazen , D. , Lichtsteiner , P. , Hafliger , P. , Delbruck , T. , Jensen , A. : Toward real-time particle tracking using an event-based dynamic vision sensor . Experiments in Fluids 51 , 1465 -- 1469 ( 2011 ) 10.1007/s00348-011-1207-y barticle

    work page doi:10.1007/s00348-011-1207-y 2011

  14. [56]

    , Morsch , R

    barticle Dacome , G. , Morsch , R. , Kotsonis , M. , Baars , W.J. : Opposition flow control for reducing skin-friction drag of a turbulent boundary layer . Physical Review Fluids 9 ( 6 ), 064602 ( 2024 ) 10.1103/PhysRevFluids.9.064602 barticle

    work page doi:10.1103/physrevfluids.9.064602 2024

  15. [57]

    , Citriniti , J.H

    bchapter Ewing , D. , Citriniti , J.H. : Examination of a LSE / POD complementary technique using single and multi-time information in the axisymmetric shear layer . In: Sorensen , J.N. , Hopfinger , E.J. , Aubry , N. (eds.) IUTAM Symposium on Simulation and Identification of Organized Structures in Flows , pp. 375 -- 384 . Springer , Dordrecht ( 1999 ). ...

    work page doi:10.1007/978-94-011-4601-2_33 1999

  16. [58]

    and Krivitzky, Eric M

    barticle Epps , B.P. , Krivitzky , E.M. : Singular value decomposition of noisy data: mode corruption . Experiments in Fluids 60 ( 8 ), 121 ( 2019 ) 10.1007/s00348-019-2761-y barticle

    work page doi:10.1007/s00348-019-2761-y 2019

  17. [59]

    , Techet , A.H

    barticle Epps , B.P. , Techet , A.H. : An error threshold criterion for singular value decomposition modes extracted from PIV data . Experiments in Fluids 48 ( 2 ), 355 -- 367 ( 2010 ) 10.1007/s00348-009-0740-4 barticle

    work page doi:10.1007/s00348-009-0740-4 2010

  18. [60]

    , Fukagata , K

    barticle Fukami , K. , Fukagata , K. , Taira , K. : Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows . Journal of Fluid Mechanics 909 , 9 ( 2021 ) 10.1017/jfm.2020.948 barticle

    work page doi:10.1017/jfm.2020.948 2021

  19. [61]

    , Willert , C.E

    barticle Franceschelli , L. , Willert , C.E. , Raiola , M. , Discetti , S. : An assessment of event-based imaging velocimetry for efficient estimation of low-dimensional coordinates in turbulent flows . Experimental Thermal and Fluid Science 164 , 111425 ( 2025 ) 10.1016/j.expthermflusci.2025.111425 barticle

    work page doi:10.1016/j.expthermflusci.2025.111425 2025

  20. [62]

    , Aider , J.-L

    barticle Gautier , N. , Aider , J.-L. , Duriez , T. , Noack , B.R. , Segond , M. , Abel , M. : Closed-loop separation control using machine learning . Journal of Fluid Mechanics 770 , 442 -- 457 ( 2015 ) 10.1017/jfm.2015.95 barticle

    work page doi:10.1017/jfm.2015.95 2015

  21. [63]

    , Delbruck , T

    barticle Gallego , G. , Delbruck , T. , Orchard , G. , Bartolozzi , C. , Taba , B. , Censi , A. , Leutenegger , S. , Davison , A.J. , Conradt , J. , Daniilidis , K. , Scaramuzza , D. : Event- Based Vision : A Survey . IEEE Transactions on Pattern Analysis and Machine Intelligence 44 ( 1 ), 154 -- 180 ( 2022 ) 10.1109/TPAMI.2020.3008413 barticle

    work page doi:10.1109/tpami.2020.3008413 2022

  22. [64]

    , George , W.K

    bchapter Glauser , M.N. , George , W.K. : Orthogonal Decomposition of the Axisymmetric Jet Mixing Layer Including Azimuthal Dependence . In: Comte-Bellot , G. , Mathieu , J. (eds.) Advances in Turbulence , pp. 357 -- 366 . Springer , Berlin, Heidelberg ( 1987 ). 10.1007/978-3-642-83045-7\_40 bchapter

    work page doi:10.1007/978-3-642-83045-7 1987

  23. [65]

    barticle Howell , J. , C. Hammarton , T. , Altmann , Y. , Jimenez , M. : High-speed particle detection and tracking in microfluidic devices using event-based sensing . Lab on a Chip 20 ( 16 ), 3024 -- 3035 ( 2020 ) 10.1039/D0LC00556H barticle

    work page doi:10.1039/d0lc00556h 2020

  24. [66]

    , Abe , C

    barticle Kanda , N. , Abe , C. , Goto , S. , Yamada , K. , Nakai , K. , Saito , Y. , Asai , K. , Nonomura , T. : Proof-of-concept study of sparse processing particle image velocimetry for real time flow observation . Experiments in Fluids 63 ( 9 ), 143 ( 2022 ) 10.1007/s00348-022-03471-0 barticle

    work page doi:10.1007/s00348-022-03471-0 2022

  25. [67]

    Journal of Basic Engineering82(1) (1960) https://doi.org/10.1115/1.3662552

    barticle Kalman , R.E. : A New Approach to Linear Filtering and Prediction Problems . Journal of Basic Engineering 82 ( 1 ), 35 -- 45 ( 1960 ) 10.1115/1.3662552 barticle

    work page doi:10.1115/1.3662552 1960

  26. [68]

    , Ratner , D

    barticle Kreizer , M. , Ratner , D. , Liberzon , A. : Real-time image processing for particle tracking velocimetry . Experiments in Fluids 48 , 105 -- 110 ( 2010 ) 10.1007/s00348-009-0715-5 barticle

    work page doi:10.1007/s00348-009-0715-5 2010

  27. [69]

    , Posch , C

    barticle Lichtsteiner , P. , Posch , C. , Delbruck , T. : A 128 times128 120 dB 15 upmus Latency Asynchronous Temporal Contrast Vision Sensor . IEEE Journal of Solid-State Circuits 43 ( 2 ), 566 -- 576 ( 2008 ) 10.1109/JSSC.2007.914337 barticle

    work page doi:10.1109/jssc.2007.914337 2008

  28. [70]

    , Gibeau , B

    barticle McCormick , F. , Gibeau , B. , Ghaemi , S. : Reactive control of velocity fluctuations using an active deformable surface and real-time PIV . Journal of Fluid Mechanics 985 , 9 ( 2024 ) 10.1017/jfm.2024.292 barticle

    work page doi:10.1017/jfm.2024.292 2024

  29. [71]

    , Mead , C

    barticle Mahowald , M.A. , Mead , C. : The silicon retina . Scientific American 264 ( 5 ), 76 -- 82 ( 1991 ) 10.1038/scientificamerican0591-76 barticle

    work page doi:10.1038/scientificamerican0591-76 1991

  30. [72]

    , Abe , C

    barticle Nonomura , T. , Abe , C. , Naramura , R. , Sasaki , Y. : Real-time feedback control of flow velocity field using sparse processing particle image velocimetry and plasma actuators . Experiments in Fluids 66 ( 7 ), 136 ( 2025 ) 10.1007/s00348-025-04039-4 barticle

    work page doi:10.1007/s00348-025-04039-4 2025

  31. [73]

    , Aider , J.-L

    botherref Pimienta , J. , Aider , J.-L. : High Resolution and High - Speed Live Optical Flow Velocimetry (2025). https://arxiv.org/abs/2509.25924v3 botherref

    work page arXiv 2025

  32. [74]

    , Discetti , S

    barticle Raiola , M. , Discetti , S. , Ianiro , A. : On PIV random error minimization with optimal POD -based low-order reconstruction . Experiments in Fluids 56 ( 4 ), 75 ( 2015 ) 10.1007/s00348-015-1940-8 barticle

    work page doi:10.1007/s00348-015-1940-8 2015

  33. [75]

    , Karlsson , S.K.F

    barticle Rajaee , M. , Karlsson , S.K.F. , Sirovich , L. : Low-dimensional description of free-shear-flow coherent structures and their dynamical behaviour . Journal of Fluid Mechanics 258 , 1 -- 29 ( 1994 ) 10.1017/S0022112094003228 barticle

    work page doi:10.1017/s0022112094003228 1994

  34. [76]

    , Rosgen , T

    bchapter Rusch , A. , Rosgen , T. : TrackAER : Real - Time Event - Based Particle Tracking . In: 14th International Symposium on Particle Image Velocimetry ( ISPIV 2021) , p. 176 . Illinois Institute of Technology , Chicago, IL ( 2021 ). 10.18409/ispiv.v1i1.176 bchapter

    work page doi:10.18409/ispiv.v1i1.176 2021

  35. [77]

    , Rosgen , T

    barticle Rusch , A. , Rosgen , T. : TrackAER : real-time event-based quantitative flow visualization . Experiments in Fluids 64 , 136 ( 2023 ) 10.1007/s00348-023-03673-0 barticle

    work page doi:10.1007/s00348-023-03673-0 2023

  36. [78]

    , Willert , C.E

    bbook Raffel , M. , Willert , C.E. , Kahler , C.J. , Scarano , F. , Wereley , S.T. , Kompenhans , J. : Particle Image Velocimetry : A Practical Guide (3rd Edition ) . Springer , Berlin Heidelberg ( 2018 ). 10.1007/978-3-319-68852-7 bbook

    work page doi:10.1007/978-3-319-68852-7 2018

  37. [79]

    , Cohen , K

    bchapter Siegel , S. , Cohen , K. , McLaughlin , T. , Myatt , J. : Real- Time Particle Image Velocimetry for Closed - Loop Flow Control Studies . In: 41st Aerospace Sciences Meeting and Exhibit , Reno ( NV ) ( 2003 ). 10.2514/6.2003-920 bchapter

    work page doi:10.2514/6.2003-920 2003

  38. [80]

    , Hamann , F

    barticle Shiba , S. , Hamann , F. , Aoki , Y. , Gallego , G. : Event- Based Background - Oriented Schlieren . IEEE Transactions on Pattern Analysis and Machine Intelligence 46 ( 4 ), 2011 -- 2026 ( 2024 ) 10.1109/TPAMI.2023.3328188 barticle

    work page doi:10.1109/tpami.2023.3328188 2011

  39. [81]

    : Turbulence and the dynamics of coherent structures

    barticle Sirovich , L. : Turbulence and the dynamics of coherent structures. I . Coherent structures . Quarterly of Applied Mathematics 45 ( 3 ), 561 -- 571 ( 1987 ) 10.1090/qam/910462 barticle

    work page doi:10.1090/qam/910462 1987

  40. [82]

    , Coiffet , F

    barticle Tinney , C.E. , Coiffet , F. , Delville , J. , Hall , A.M. , Jordan , P. , Glauser , M.N. : On spectral linear stochastic estimation . Experiments in Fluids 41 ( 5 ), 763 -- 775 ( 2006 ) 10.1007/s00348-006-0199-5 barticle

    work page doi:10.1007/s00348-006-0199-5 2006

  41. [83]

    , Griffin , J

    barticle Tu , J.H. , Griffin , J. , Hart , A. , Rowley , C.W. , Cattafesta , L.N. , Ukeiley , L.S. : Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of velocity fields . Experiments in Fluids 54 ( 2 ), 1429 ( 2013 ) 10.1007/s00348-012-1429-7 barticle

    work page doi:10.1007/s00348-012-1429-7 2013

  42. [84]

    , Ianiro , A

    barticle Tirelli , I. , Ianiro , A. , Discetti , S. : An end-to-end KNN -based PTV approach for high-resolution measurements and uncertainty quantification . Experimental Thermal and Fluid Science 140 , 110756 ( 2023 ) 10.1016/j.expthermflusci.2022.110756 barticle

    work page doi:10.1016/j.expthermflusci.2022.110756 2023

  43. [85]

    , Aider , J.-L

    botherref Varon , E. , Aider , J.-L. , Eulalie , Y. , Edwige , S. , Gilotte , P. : Adaptive control of the dynamics of a fully turbulent bimodal wake using real-time PIV . Experiments in Fluids 60 (2019) 10.1007/s00348-019-2766-6 botherref

    work page doi:10.1007/s00348-019-2766-6 2019

  44. [86]

    , Naramura , R

    botherref Viguera , R. , Naramura , R. , Sasaki , Y. , Nonomura , T. : Adaptive control pattern for real-time-visual-feedback flow separation control over airfoil with sparse processing particle image velocimetry and plasma actuator. Experiments in Fluids 67 (2026) 10.1007/s00348-026-04175-5 botherref

    work page doi:10.1007/s00348-026-04175-5 2026

  45. [87]

    , Bishop , G

    botherref Welch , G. , Bishop , G. : An Introduction to the Kalman Filter (1995). https://www.cs.unc.edu/ welch/media/pdf/kalman_intro.pdf botherref

    1995

  46. [88]

    , Franceschelli , L

    barticle Willert , C. , Franceschelli , L. , Amico , E. , Raiola , M. , Cafiero , G. , Discetti , S. : Real-time event-based particle image velocimetry for active flow control . Journal of Physics: Conference Series 3173 ( 1 ), 012001 ( 2026 ) 10.1088/1742-6596/3173/1/012001 barticle

    work page doi:10.1088/1742-6596/3173/1/012001 2026

  47. [89]

    : Event-based imaging velocimetry using pulsed illumination

    barticle Willert , C. : Event-based imaging velocimetry using pulsed illumination . Experiments in Fluids 64 , 98 ( 2023 ) 10.1007/s00348-023-03641-8 barticle

    work page doi:10.1007/s00348-023-03641-8 2023

  48. [90]

    : Event-based particle image velocimetry for high-speed flows

    barticle Willert , C. : Event-based particle image velocimetry for high-speed flows . Measurement Science and Technology 36 ( 7 ), 075302 ( 2025 ) 10.1088/1361-6501/ade27a barticle

    work page doi:10.1088/1361-6501/ade27a 2025

  49. [91]

    , Munson , M

    bchapter Willert , C. , Munson , M. , Gharib , M. : Real- Time Particle Image Velocimetry for Closed - Loop Flow Control Applications . In: 15th International Symposium on Applications of Laser Techniques to Fluid Mechanics ( 2010 ). https://elib.dlr.de/64688/ bchapter

    2010