pith. sign in

arxiv: 2605.19160 · v1 · pith:RSSGVFEOnew · submitted 2026-05-18 · 📡 eess.IV · physics.comp-ph· physics.data-an· physics.optics

An evaluation framework for sparse 4D (3D + time) imaging reconstruction via bootstrapped cross-validation

Yuhe Zhang , Zisheng Yao , Zhe Hu , Tobias Ritschel , Pablo Villanueva-Perez This is my paper

Pith reviewed 2026-05-20 06:54 UTC · model grok-4.3

classification 📡 eess.IV physics.comp-phphysics.data-anphysics.optics
keywords 4D imagingsparse reconstructionbootstrapped cross-validationdeep learningX-ray imagingimage evaluationultrafast imagingreconstruction assessment
0
0 comments X

The pith

Bootstrapped cross-validation estimates 4D reconstruction quality from sparse data without ground truth by measuring correlations across data subsets.

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

The paper proposes a new evaluation framework for assessing how well deep learning methods reconstruct 4D images from limited measurements. It works by dividing the acquired data into independent subsets, reconstructing each separately, and then calculating correlations between those reconstructions. High agreement suggests the method is reliably capturing the true dynamics, while low agreement indicates potential issues. This approach is particularly useful for ultrafast X-ray imaging of dynamic processes like droplet collisions where no perfect reference exists. It draws from similar validation techniques used in cryo-electron microscopy.

Core claim

The bootstrapped cross-validation framework estimates reconstruction performance in the absence of ground truth by quantifying correlations between reconstructions generated from independently sampled subsets of the acquired sparse 4D data. This provides both qualitative and quantitative assessment and was tested on simulated water droplet collision experiments using the 4D-ONIX deep-learning method for sparse and ultra-sparse X-ray datasets.

What carries the argument

Bootstrapped cross-validation that splits the measured data into subsets, reconstructs from each, and uses correlation as a proxy for fidelity to the true 4D object.

If this is right

  • Reconstruction performance can be assessed qualitatively and quantitatively without a 4D reference.
  • Supports informed decisions on experimental strategies in ultrafast imaging.
  • Applies to deep learning methods for reconstructing from sparse spatiotemporal measurements.
  • Validated in scenarios with water droplet collisions in X-ray imaging.

Where Pith is reading between the lines

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

  • This framework might generalize to evaluate reconstructions in other sparse imaging domains like medical CT or astronomy.
  • If subset correlations reliably predict error, algorithms could be tuned to maximize such agreement during development.
  • Real-world adoption could reduce reliance on expensive or impossible ground truth acquisitions in dynamic imaging studies.

Load-bearing premise

Agreement between reconstructions from independently sampled data subsets serves as a faithful proxy for how accurately each reconstruction matches the true underlying 4D object.

What would settle it

In simulations where ground truth is known, if the correlation scores from the framework do not correspond to the actual reconstruction errors measured against ground truth, the method would be shown ineffective as a proxy.

Figures

Figures reproduced from arXiv: 2605.19160 by Pablo Villanueva-Perez, Tobias Ritschel, Yuhe Zhang, Zhe Hu, Zisheng Yao.

Figure 1
Figure 1. Figure 1: Schematic of the bootstrapped cross-validation framework. (a) Illustration of the workflow [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: The corresponding reconstruction yˆ i(k) = F i(k) [P i(k) ] is therefore a random estimator of the true 4D object y. Consider a pairwise cross-validation estimator, with yˆ i(k) a and yˆ i(k) b be two indepen￾dent reconstructions from the two independent sampled subsets P i(k) a and P i(k) b . The cross-validation metric is defined as C = M(yˆ i(k) a , yˆ i(k) b ), (4) where M(·, ·) denotes a 4D evaluation… view at source ↗
Figure 2
Figure 2. Figure 2: Performance evaluation of 4D reconstructions under sparse spatial sampling. The performance [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Performance evaluation of 4D reconstructions under ultra-sparse spatial sampling. The per [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

Four-dimensional (4D; 3D + time) microscopic imaging has emerged as a powerful technique for investigating dynamic phenomena in complex systems, enabling direct visualization of structural evolution in space and time. However, when pushing the limits of spatiotemporal resolution, most time-resolved imaging techniques yield inherently sparse 4D datasets. While deep learning-based reconstruction methods have shown promise in reconstructing 4D from sparse spatiotemporal measurements, a practical approach for evaluating their performance in the absence of a 4D reference has, to the best of our knowledge, been lacking. Here, we present a bootstrapped cross-validation framework that estimates reconstruction performance by quantifying correlations between reconstructions generated from independently sampled subsets of the acquired data, as inspired by the 3D validation strategy in cryo-electron microscopy, where reconstructions from split datasets are compared to assess resolutions. This enables both qualitative and quantitative assessment in the absence of ground truth. We investigate two representative scenarios with sparse and ultra-sparse X-ray datasets and validate this approach using 4D-ONIX, a 4D deep-learning reconstruction method, on simulated water droplet collision experiments. The proposed approach provides a reference-free framework for performance estimation and support for better-informed experimental strategies across a wide range of ultrafast imaging 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 manuscript proposes a bootstrapped cross-validation framework for evaluating deep-learning reconstructions of sparse and ultra-sparse 4D (3D+time) imaging data in the absence of ground truth. Reconstructions are generated from independently sampled subsets of the measured data, and their mutual correlations are used as a proxy for reconstruction quality; the approach is inspired by split-dataset resolution assessment in cryo-EM and is demonstrated on simulated water-droplet collision experiments using the 4D-ONIX reconstructor.

Significance. If the central proxy assumption holds after proper calibration, the framework would supply a practical, reference-free tool for both qualitative and quantitative performance estimation in ultrafast X-ray and related 4D imaging modalities where ground truth is unavailable. The explicit link to cryo-EM practice and the use of controlled simulated data are constructive elements that could help guide experimental design across a range of sparse spatiotemporal imaging applications.

major comments (2)
  1. [Abstract] Abstract: the central claim that subset-correlation provides a faithful quantitative proxy for fidelity to the unknown true 4D object is load-bearing, yet the abstract reports no numerical correlation values, no error analysis, and no explicit regression of the proxy metric against ground-truth quantities (voxel-wise MSE, SSIM, etc.) across sparsity levels in the simulated droplet data. Without this calibration the transfer to true no-GT settings remains untested.
  2. [Validation section] Validation on simulated droplet collisions: the skeptic concern is material here—if the 4D-ONIX network learns consistent biases from the full measurement statistics, high inter-subset correlation can occur even when absolute accuracy is low. The manuscript must therefore show that the observed correlation tracks actual reconstruction error magnitude (or at least does not systematically overestimate fidelity) before the quantitative-assessment claim can be accepted.
minor comments (2)
  1. Clarify the precise bootstrapping or splitting procedure (number of subsets, sampling strategy in the ultra-sparse regime) so that readers can judge whether representative data variations are captured.
  2. Add a short discussion of potential failure modes (e.g., when the reconstructor exhibits strong consistent bias) to strengthen the limitations paragraph.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments highlight important aspects of calibration and validation that we address below. We outline revisions that will strengthen the manuscript without altering its core contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that subset-correlation provides a faithful quantitative proxy for fidelity to the unknown true 4D object is load-bearing, yet the abstract reports no numerical correlation values, no error analysis, and no explicit regression of the proxy metric against ground-truth quantities (voxel-wise MSE, SSIM, etc.) across sparsity levels in the simulated droplet data. Without this calibration the transfer to true no-GT settings remains untested.

    Authors: We agree that the abstract would benefit from explicit quantitative support for the proxy metric. The full manuscript already contains the requested regressions and error analyses on the simulated droplet data (comparing subset correlations to voxel-wise MSE and SSIM across sparsity levels), but these are not summarized numerically in the abstract. We will revise the abstract to include representative correlation values and a brief statement of the observed regression performance, thereby providing the calibration evidence directly in the abstract. revision: yes

  2. Referee: [Validation section] Validation on simulated droplet collisions: the skeptic concern is material here—if the 4D-ONIX network learns consistent biases from the full measurement statistics, high inter-subset correlation can occur even when absolute accuracy is low. The manuscript must therefore show that the observed correlation tracks actual reconstruction error magnitude (or at least does not systematically overestimate fidelity) before the quantitative-assessment claim can be accepted.

    Authors: We share this concern and have used the simulated droplet data precisely to test it. Because ground truth is available, we directly compare inter-subset correlations against voxel-wise reconstruction errors computed from the known true object. The existing validation already demonstrates that higher correlations correspond to lower errors and that the proxy does not systematically overestimate fidelity within the tested sparsity regimes. To make this relationship more explicit and address the skeptic concern head-on, we will add a dedicated panel or supplementary table showing the correlation-versus-error scatter and associated regression statistics. revision: partial

Circularity Check

0 steps flagged

No significant circularity; framework is a self-contained methodological proposal validated externally

full rationale

The paper proposes a bootstrapped cross-validation approach that quantifies correlations between reconstructions from independently sampled data subsets to estimate performance without ground truth, drawing inspiration from established cryo-EM split-dataset practices. This is a standard statistical validation technique rather than a derivation that reduces to its own inputs by construction. No equations, fitted parameters, or predictions are presented that equate to the method itself; validation occurs on simulated droplet collision data with available ground truth, providing independent external benchmarking. No self-citations are load-bearing for the core premise, no uniqueness theorems are imported from prior author work, and no ansatzes are smuggled in. The central claim therefore remains self-contained and does not exhibit circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on a single domain assumption about subset agreement proxying true accuracy; no free parameters or new physical entities are introduced.

axioms (1)
  • domain assumption Agreement between reconstructions from independently sampled data subsets reliably indicates reconstruction fidelity to the true 4D object
    This is the central premise that allows the method to operate without ground truth; it is stated in the abstract as the basis for both qualitative and quantitative assessment.

pith-pipeline@v0.9.0 · 5778 in / 1278 out tokens · 49291 ms · 2026-05-20T06:54:43.036372+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

72 extracted references · 72 canonical work pages

  1. [1]

    4d electron tomography.Science, 328(5986):1668–1673, 2010

    Oh-Hoon Kwon and Ahmed H Zewail. 4d electron tomography.Science, 328(5986):1668–1673, 2010

    work page 2010

  2. [2]

    4d microvascular imaging based on ultrafast doppler tomography.Neuroimage, 127:472–483, 2016

    Charlie Demen´ e, Elodie Tiran, Lim-Anna Sieu, Antoine Bergel, Jean Luc Gennisson, Mathieu Per- not, Thomas Deffieux, Ivan Cohen, and Mickael Tanter. 4d microvascular imaging based on ultrafast doppler tomography.Neuroimage, 127:472–483, 2016

    work page 2016

  3. [3]

    Exploring frontiers of 4d x-ray tomography

    Wataru Yashiro, Wolfgang Voegeli, and Hiroyuki Kudo. Exploring frontiers of 4d x-ray tomography. Applied Sciences, 11(19):8868, 2021

    work page 2021

  4. [4]

    Dynamic ct reconstruction with improved temporal resolution for scanning of fluid flow in porous media.Water Resources Research, 58(4):e2021WR031365, 2022

    Wannes Goethals, Tom Bultreys, Zaira Manigrasso, Arjen Mascini, Jan Aelterman, and Matthieu N Boone. Dynamic ct reconstruction with improved temporal resolution for scanning of fluid flow in porous media.Water Resources Research, 58(4):e2021WR031365, 2022

    work page 2022

  5. [5]

    Nuts and bolts of 4d-mri for radiotherapy

    Bjorn Stemkens, Eric S Paulson, and Rob HN Tijssen. Nuts and bolts of 4d-mri for radiotherapy. Physics in Medicine & Biology, 63(21):21TR01, 2018

    work page 2018

  6. [6]

    Magnetic resonance-guided radiation therapy: a review.Journal of medical imaging and radiation oncology, 64(1):163–177, 2020

    Stephen Chin, Cynthia L Eccles, Alan McWilliam, Robert Chuter, Emma Walker, Philip White- hurst, Joseph Berresford, Marcel Van Herk, Peter J Hoskin, and Ananya Choudhury. Magnetic resonance-guided radiation therapy: a review.Journal of medical imaging and radiation oncology, 64(1):163–177, 2020

    work page 2020

  7. [7]

    Four-dimensional computational ultrasound imaging of brain hemodynamics.Science ad- vances, 10(3):eadk7957, 2024

    Michael D Brown, Bastian S Generowicz, Stephanie Dijkhuizen, Sebastiaan KE Koekkoek, Christos Strydis, Johannes G Bosch, Petros Arvanitis, Geert Springeling, Geert JT Leus, Chris I De Zeeuw, et al. Four-dimensional computational ultrasound imaging of brain hemodynamics.Science ad- vances, 10(3):eadk7957, 2024

    work page 2024

  8. [8]

    4d electron microscopy: principles and applications

    David J Flannigan and Ahmed H Zewail. 4d electron microscopy: principles and applications. Accounts of chemical research, 45(10):1828–1839, 2012

    work page 2012

  9. [9]

    Live optical projection tomography.Organogenesis, 5(4):211–216, 2009

    Jean-Fran¸ cois Colas and James Sharpe. Live optical projection tomography.Organogenesis, 5(4):211–216, 2009

    work page 2009

  10. [10]

    Toward a diffraction limited light source.Physical Review Accelerators and Beams, 26(2):021601, 2023

    Pantaleo Raimondi and Simone Maria Liuzzo. Toward a diffraction limited light source.Physical Review Accelerators and Beams, 26(2):021601, 2023. 10

    work page 2023

  11. [11]

    New op- portunities for time-resolved imaging using diffraction-limited storage rings.Synchrotron Radiation, 31(5), 2024

    Zisheng Yao, Julia Rogalinski, Eleni Myrto Asimakopoulou, Yuhe Zhang, Korneliya Gordeyeva, Zhaleh Atoufi, Hanna Dierks, Samuel McDonald, Stephen Hall, Jesper Wallentin, et al. New op- portunities for time-resolved imaging using diffraction-limited storage rings.Synchrotron Radiation, 31(5), 2024

    work page 2024

  12. [12]

    Megahertz x-ray microscopy at x-ray free-electron laser and synchrotron sources.Optica, 6(9):1106–1109, 2019

    Patrik Vagoviˇ c, Tokushi Sato, Ladislav Mikeˇ s, Grant Mills, Rita Graceffa, Frans Mattsson, Pablo Villanueva-Perez, Alexey Ershov, Tom´ aˇ s Farag´ o, Jozef Uliˇ cn` y, et al. Megahertz x-ray microscopy at x-ray free-electron laser and synchrotron sources.Optica, 6(9):1106–1109, 2019

    work page 2019

  13. [13]

    Gigafrost: the gigabit fast readout system for tomography.Synchrotron Radiation, 24(6):1250–1259, 2017

    Rajmund Mokso, Christian M Schlep¨ utz, Gerd Theidel, Heiner Billich, Elmar Schmid, Tine Celcer, Gordan Mikuljan, Leonardo Sala, Federica Marone, Nick Schlumpf, et al. Gigafrost: the gigabit fast readout system for tomography.Synchrotron Radiation, 24(6):1250–1259, 2017

    work page 2017

  14. [14]

    I see what you do not see: The world observed with high-speed cameras.Complexity and Synergetics, pages 361–371, 2018

    Kinko Tsuji. I see what you do not see: The world observed with high-speed cameras.Complexity and Synergetics, pages 361–371, 2018

    work page 2018

  15. [15]

    springer, 2018

    Markus Raffel, Christian E Willert, Fulvio Scarano, Christian J K¨ ahler, Steve T Wereley, and J¨ urgen Kompenhans.Particle image velocimetry: a practical guide. springer, 2018

    work page 2018

  16. [16]

    Stereoscopic piv measurements using low-cost action cameras.Experiments in Fluids, 62(3):57, 2021

    Theo K¨ aufer, J¨ org K¨ onig, and Christian Cierpka. Stereoscopic piv measurements using low-cost action cameras.Experiments in Fluids, 62(3):57, 2021

    work page 2021

  17. [17]

    High speed particle image velocimetry and particle tracking methods in reactive and non- reactive flows

    Daniel K Lauriola, Mateo Gomez, Terrence R Meyer, Steven F Son, Mikhail Slipchenko, and Sukesh Roy. High speed particle image velocimetry and particle tracking methods in reactive and non- reactive flows. InAIAA Scitech 2019 Forum, page 1605, 2019

    work page 2019

  18. [18]

    High resolution volumetric dual-camera light-field piv.Experiments in Fluids, 60(8):132, 2019

    Di Mei, Junfei Ding, Shengxian Shi, Tze How New, and Julio Soria. High resolution volumetric dual-camera light-field piv.Experiments in Fluids, 60(8):132, 2019

    work page 2019

  19. [19]

    Megahertz x-ray multi-projection imaging.arXiv preprint arXiv:2305.11920, 2023

    Pablo Villanueva-Perez, Valerio Bellucci, Yuhe Zhang, Sarlota Birnsteinova, Rita Graceffa, Luigi Adriano, Eleni Myrto Asimakopoulou, Ilia Petrov, Zisheng Yao, Marco Romagnoni, et al. Megahertz x-ray multi-projection imaging.arXiv preprint arXiv:2305.11920, 2023

    work page arXiv 2023

  20. [20]

    Tomoscopy: Time-resolved tomography for dynamic processes in materials

    Francisco Garc´ ıa-Moreno, Paul Hans Kamm, Tillmann Robert Neu, Felix B¨ ulk, Mike Andreas Noack, Mareike Wegener, Nadine von der Eltz, Christian Matthias Schlep¨ utz, Marco Stampanoni, and John Banhart. Tomoscopy: Time-resolved tomography for dynamic processes in materials. Advanced Materials, 33(45):2104659, 2021

    work page 2021

  21. [21]

    High-speed, 3d volumetric displacement and strain mapping in soft materials using light field mi- croscopy.Experimental Mechanics, 62(9):1673–1690, 2022

    Selda Buyukozturk, AK Landauer, LA Summey, AN Chukwu, Jing Zhang, and Christian Franck. High-speed, 3d volumetric displacement and strain mapping in soft materials using light field mi- croscopy.Experimental Mechanics, 62(9):1673–1690, 2022

    work page 2022

  22. [22]

    Ultrasound cav- itation and exfoliation dynamics of 2d materials re-vealed in operando by x-ray free electron laser megahertz imaging.arXiv preprint arXiv:2305.08538, 2023

    Kang Xiang, Shi Huang, Hongyuan Song, Vasilii Bazhenov, Valerio Bellucci, Sarlota Birnsteinova, Raphael de Wijn, Jayanath CP Koliyadu, Faisal HM Koua, Adam Round, et al. Ultrasound cav- itation and exfoliation dynamics of 2d materials re-vealed in operando by x-ray free electron laser megahertz imaging.arXiv preprint arXiv:2305.08538, 2023

    work page arXiv 2023

  23. [23]

    HC Wang, K Liu, B Lukic, WR Hu, CH Braithwaite, J Zhao, A Rack, and QB Zhang. In-situ deformation and fracturing characteristics of geomaterials under dynamic loading: insights from ultra-high-speed x-ray phase contrast imaging and dem modelling.International Journal of Rock Mechanics and Mining Sciences, 175:105656, 2024

    work page 2024

  24. [24]

    Using x-ray tomoscopy to explore the dynamics of foaming metal.Nature communications, 10(1):3762, 2019

    Francisco Garc´ ıa-Moreno, Paul Hans Kamm, Tillmann Robert Neu, Felix B¨ ulk, Rajmund Mokso, Christian Matthias Schlep¨ utz, Marco Stampanoni, and John Banhart. Using x-ray tomoscopy to explore the dynamics of foaming metal.Nature communications, 10(1):3762, 2019

    work page 2019

  25. [25]

    Communication in the presence of noise.Proceedings of the IRE, 37(1):10–21, 2006

    Claude E Shannon. Communication in the presence of noise.Proceedings of the IRE, 37(1):10–21, 2006

    work page 2006

  26. [26]

    Cambridge University Press, 2019

    Chris Jacobsen.X-ray Microscopy. Cambridge University Press, 2019

    work page 2019

  27. [27]

    Operando tomographic microscopy during laser-based powder bed fusion of alumina.Communica- tions Materials, 4(1):73, 2023

    Malgorzata G Makowska, Fabrizio Verga, Stefan Pfeiffer, Federica Marone, Cynthia ST Chang, Kevin Florio, Christian M Schlep¨ utz, Konrad Wegener, Thomas Graule, and Steven Van Petegem. Operando tomographic microscopy during laser-based powder bed fusion of alumina.Communica- tions Materials, 4(1):73, 2023. 11

    work page 2023

  28. [28]

    Lund University, 2024

    Yuhe Zhang.Advancing X-ray imaging with deep learning: Physics-inspired reconstruction ap- proaches. Lund University, 2024

    work page 2024

  29. [29]

    Development of an x-ray real-time stereo imaging technique using synchrotron radiation.Journal of synchrotron radiation, 18(4):569–574, 2011

    Masato Hoshino, Kentaro Uesugi, James Pearson, Takashi Sonobe, Mikiyasu Shirai, and Naoto Yagi. Development of an x-ray real-time stereo imaging technique using synchrotron radiation.Journal of synchrotron radiation, 18(4):569–574, 2011

    work page 2011

  30. [30]

    Dual beam microfocus high-energy tomography: Towards multimodal and faster laboratory experiments.Tomography of Materials and Structures, 5:100030, 2024

    Eric Maire, Gabriel Bonnard, J´ erˆ ome Adrien, Xavier Boulnat, Jean Michel L´ etang, and Jo¨ el Lacham- bre. Dual beam microfocus high-energy tomography: Towards multimodal and faster laboratory experiments.Tomography of Materials and Structures, 5:100030, 2024

    work page 2024

  31. [31]

    Single-shot x-ray stereo imaging based on dual polycapillary parallel x-ray lenses.Optics Letters, 50(17):5298–5301, 2025

    Shangkun Shao, Tianyu Yuan, Chengbo Li, Xingyi Wang, Lu Hua, Yuchuan Zhong, Jinyue Hu, Mengfang Chen, Xuepeng Sun, and Tianxi Sun. Single-shot x-ray stereo imaging based on dual polycapillary parallel x-ray lenses.Optics Letters, 50(17):5298–5301, 2025

    work page 2025

  32. [32]

    Development of x-ray triscopic imaging system towards three-dimensional measurements of dynamical samples.Journal of Instrumentation, 8(05):C05002, 2013

    M Hoshino, T Sera, K Uesugi, and N Yagi. Development of x-ray triscopic imaging system towards three-dimensional measurements of dynamical samples.Journal of Instrumentation, 8(05):C05002, 2013

    work page 2013

  33. [33]

    Hard x-ray multi-projection imaging for single-shot approaches

    P Villanueva-Perez, B Pedrini, R Mokso, P Vagovic, VA Guzenko, SJ Leake, PR Willmott, P Oberta, C David, HN Chapman, et al. Hard x-ray multi-projection imaging for single-shot approaches. Optica, 5(12):1521–1524, 2018

    work page 2018

  34. [34]

    Multibeam x-ray optical system for high-speed tomography.Optica, 7(5):514– 517, 2020

    Wolfgang Voegeli, Kentaro Kajiwara, Hiroyuki Kudo, Tetsuroh Shirasawa, Xiaoyu Liang, and Wataru Yashiro. Multibeam x-ray optical system for high-speed tomography.Optica, 7(5):514– 517, 2020

    work page 2020

  35. [35]

    Three-dimensional coherent diffraction snapshot imaging using extreme-ultraviolet radiation from a free electron laser.Optica, 10(8):1053–1058, 2023

    Danny Fainozzi, Matteo Ippoliti, Fulvio Bille, Dario De Angelis, Laura Foglia, Claudio Masciovec- chio, Riccardo Mincigrucci, Matteo Pancaldi, Emanuele Pedersoli, Christian M G¨ unther, et al. Three-dimensional coherent diffraction snapshot imaging using extreme-ultraviolet radiation from a free electron laser.Optica, 10(8):1053–1058, 2023

    work page 2023

  36. [36]

    Development towards high-resolution khz-speed rotation-free volumetric imaging.Optics Express, 32(3):4413– 4426, 2024

    Eleni Myrto Asimakopoulou, Valerio Bellucci, Sarlota Birnsteinova, Zisheng Yao, Yuhe Zhang, Ilia Petrov, Carsten Deiter, Andrea Mazzolari, Marco Romagnoni, Dusan Korytar, et al. Development towards high-resolution khz-speed rotation-free volumetric imaging.Optics Express, 32(3):4413– 4426, 2024

    work page 2024

  37. [37]

    McDonald, Kim Nyg˚ ard, Eleni Myrto Asimakopoulou, and Pablo Villanueva-Perez

    Julia Katharina Rogalinski, Zisheng Yao, Yuhe Zhang, Zhe Hu, Korneliya Gordeyeva, Tomas Ros´ en, Daniel S¨ oderberg, Andrea Mazzolari, Jackson da Silva, Vahid Haghighat, Samuel A. McDonald, Kim Nyg˚ ard, Eleni Myrto Asimakopoulou, and Pablo Villanueva-Perez. Time-resolved 3d imaging opportunities with xmpi at formax, 2025

    work page 2025

  38. [38]

    Real time volumetric ultrasound imaging system.Journal of Digital Imaging, 3(4):261–266, 1990

    Olaf T von Ramm and Stephen W Smith. Real time volumetric ultrasound imaging system.Journal of Digital Imaging, 3(4):261–266, 1990

    work page 1990

  39. [39]

    Mi- croscopic optical projection tomography in vivo.PLOS one, 6(4):e18963, 2011

    Matthias Rieckher, Udo Jochen Birk, Heiko Meyer, Jorge Ripoll, and Nektarios Tavernarakis. Mi- croscopic optical projection tomography in vivo.PLOS one, 6(4):e18963, 2011

    work page 2011

  40. [40]

    Unsupervised machine learning combined with 4d scanning transmission electron microscopy for bimodal nanostructural analysis.Scientific Reports, 14(1):2901, 2024

    Koji Kimoto, Jun Kikkawa, Koji Harano, Ovidiu Cretu, Yuki Shibazaki, and Fumihiko Uesugi. Unsupervised machine learning combined with 4d scanning transmission electron microscopy for bimodal nanostructural analysis.Scientific Reports, 14(1):2901, 2024

    work page 2024

  41. [41]

    4d-onix for reconstructing 3d movies from sparse x-ray projections via deep learning.Communications Engineering, 4(1):1–12, 2025

    Yuhe Zhang, Zisheng Yao, Robert Kl¨ ofkorn, Tobias Ritschel, and Pablo Villanueva-Perez. 4d-onix for reconstructing 3d movies from sparse x-ray projections via deep learning.Communications Engineering, 4(1):1–12, 2025

    work page 2025

  42. [42]

    Super time-resolved tomography.Advanced Science, page e11933, 2025

    Zhe Hu, Zisheng Yao, Kalle Josefsson, Francisco Garc´ ıa-Moreno, Malgorzata Makowska, Yuhe Zhang, and Pablo Villanueva-Perez. Super time-resolved tomography.Advanced Science, page e11933, 2025

    work page 2025

  43. [43]

    Implicit neural representation for fast 4d computed tomography of multiphase flow in porous media.Communications Physics, 8(1):339, 2025

    Henrik Friis, H˚ akon Nese, Giacomo Luani, Colin Pryme, Lars Rennan, Basab Chattopadhyay, An- ders Kristoffersen, Ole Jakob Mengshoel, and Dag Werner Breiby. Implicit neural representation for fast 4d computed tomography of multiphase flow in porous media.Communications Physics, 8(1):339, 2025. 12

    work page 2025

  44. [44]

    Nert-ca: Efficient dy- namic reconstruction from sparse-view x-ray coronary angiography

    Kirsten WH Maas, Danny Ruijters, Nicola Pezzotti, and Anna Vilanova. Nert-ca: Efficient dy- namic reconstruction from sparse-view x-ray coronary angiography. InInternational Workshop on Reconstruction and Imaging Motion Estimation, pages 13–22. Springer, 2025

    work page 2025

  45. [45]

    Deep learning enhanced light sheet fluorescence microscopy for in vivo 4d imaging of zebrafish heart beating.Light: Science & Applications, 14(1):92, 2025

    Meng Zhang, Renjian Li, Songnian Fu, Sunil Kumar, James Mcginty, Yuwen Qin, and Lingling Chen. Deep learning enhanced light sheet fluorescence microscopy for in vivo 4d imaging of zebrafish heart beating.Light: Science & Applications, 14(1):92, 2025

    work page 2025

  46. [46]

    Four-dimensional materials science: Time-resolved x-ray mi- crocomputed tomography.MRS Bulletin, pages 1–18, 2025

    Nikhilesh Chawla and Eshan Ganju. Four-dimensional materials science: Time-resolved x-ray mi- crocomputed tomography.MRS Bulletin, pages 1–18, 2025

    work page 2025

  47. [47]

    Rankiqa: Learning from rankings for no-reference image quality assessment

    Xialei Liu, Joost Van De Weijer, and Andrew D Bagdanov. Rankiqa: Learning from rankings for no-reference image quality assessment. InProceedings of the IEEE international conference on computer vision, pages 1040–1049, 2017

    work page 2017

  48. [48]

    Hallucinated-iqa: No-reference image quality assessment via adversarial learning

    Kwan-Yee Lin and Guanxiang Wang. Hallucinated-iqa: No-reference image quality assessment via adversarial learning. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 732–741, 2018

    work page 2018

  49. [49]

    Crossscore: Towards multi-view image evaluation and scoring

    Zirui Wang, Wenjing Bian, and Victor Adrian Prisacariu. Crossscore: Towards multi-view image evaluation and scoring. InEuropean Conference on Computer Vision, pages 492–510. Springer, 2024

    work page 2024

  50. [50]

    Number 95

    Christopher Z Mooney, Robert D Duval, and Robert Duvall.Bootstrapping: A nonparametric approach to statistical inference. Number 95. sage, 1993

    work page 1993

  51. [51]

    Similarity measures between images.Ultramicroscopy, 21(1):95–100, 1987

    Marin Van Heel. Similarity measures between images.Ultramicroscopy, 21(1):95–100, 1987

    work page 1987

  52. [52]

    Prevention of overfitting in cryo-em structure determination

    Sjors HW Scheres and Shaoxia Chen. Prevention of overfitting in cryo-em structure determination. Nature methods, 9(9):853–854, 2012

    work page 2012

  53. [53]

    X-ray in-line holography and holotomography at the nanomax beamline.Synchrotron Radiation, 29(1):224–229, 2022

    and others. X-ray in-line holography and holotomography at the nanomax beamline.Synchrotron Radiation, 29(1):224–229, 2022

    work page 2022

  54. [54]

    Hosseini, Stefan Turek, Matthias M¨ oller, and Christian Palmes

    Babak S. Hosseini, Stefan Turek, Matthias M¨ oller, and Christian Palmes. Isogeometric analysis of the navier–stokes–cahn–hilliard equations with application to incompressible two-phase flows. Journal of Computational Physics, 348:171–194, 2017

    work page 2017

  55. [55]

    Dettmer, and Djordje Peri’c

    Aleksander Lovri’c, Wulf G. Dettmer, and Djordje Peri’c. Low order finite element methods for the navier-stokes-cahn-hilliard equations.arXiv: Computational Physics, 2019

    work page 2019

  56. [56]

    Nerf-ca: Dynamic re- construction of x-ray coronary angiography with extremely sparse-views.IEEE Transactions on Visualization and Computer Graphics, 2025

    Kirsten WH Maas, Danny Ruijters, Anna Vilanova, and Nicola Pezzotti. Nerf-ca: Dynamic re- construction of x-ray coronary angiography with extremely sparse-views.IEEE Transactions on Visualization and Computer Graphics, 2025

    work page 2025

  57. [57]

    Dyrect com- puted tomography: Dynamic reconstruction of events on a continuous timescale.IEEE Transactions on Computational Imaging, 2025

    Wannes Goethals, Tom Bultreys, Steffen Berg, Matthieu N Boone, and Jan Aelterman. Dyrect com- puted tomography: Dynamic reconstruction of events on a continuous timescale.IEEE Transactions on Computational Imaging, 2025

    work page 2025

  58. [58]

    Weihao Yu, Yuanhao Cai, Ruyi Zha, Zhiwen Fan, Chenxin Li, and Yixuan Yuan.x 2-gaussian: 4d radiative gaussian splatting for continuous-time tomographic reconstruction.arXiv preprint arXiv:2503.21779, 2025

    work page arXiv 2025

  59. [59]

    HJ Nitzpon, JC Rajaonah, CB Burckhardt, B Dousse, and JJ Meister. A new pulsed wave doppler ultrasound system to measure blood velocities beyond the nyquist limit.IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 42(2):265–279, 2002

    work page 2002

  60. [60]

    Estimation of doppler velocities from sub-nyquist ultra-wideband radar measurements.IEEE Sensors Journal, 16(23):8557–8565, 2016

    Takuya Sakamoto, Akihiko Matsuoka, and Hidekuni Yomo. Estimation of doppler velocities from sub-nyquist ultra-wideband radar measurements.IEEE Sensors Journal, 16(23):8557–8565, 2016

    work page 2016

  61. [61]

    Physics-informed 4d x-ray image reconstruction from ultra-sparse spatiotemporal data.Measure- ment Science and Technology, 36(8):085403, aug 2025

    Zisheng Yao, Yuhe Zhang, Zhe Hu, Robert Kl¨ ofkorn, Tobias Ritschel, and Pablo Villanueva-Perez. Physics-informed 4d x-ray image reconstruction from ultra-sparse spatiotemporal data.Measure- ment Science and Technology, 36(8):085403, aug 2025. 13

    work page 2025

  62. [62]

    Raissi, P

    M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707, 2019

    work page 2019

  63. [63]

    Fluidnexus: 3d fluid reconstruction and prediction from a single video

    Yue Gao, Hong-Xing Yu, Bo Zhu, and Jiajun Wu. Fluidnexus: 3d fluid reconstruction and prediction from a single video. InProceedings of the Computer Vision and Pattern Recognition Conference, pages 26091–26101, 2025

    work page 2025

  64. [64]

    Fourier shell correlation threshold criteria.Journal of Structural Biology, 151(3):250 – 262, 2005

    Marin van Heel and Michael Schatz. Fourier shell correlation threshold criteria.Journal of Structural Biology, 151(3):250 – 262, 2005

    work page 2005

  65. [65]

    4d water droplet collision datasets

    Yuhe Zhang, Zisheng Yao, Robert Kl¨ ofkorn, Tobias Ritschel, and Pablo Villanueva-Perez. 4d water droplet collision datasets. figsharehttps://doi.org/10.6084/m9.figshare.28533098(2025)

    work page doi:10.6084/m9.figshare.28533098(2025 2025

  66. [66]

    Bastian, M

    P. Bastian, M. Blatt, M. Dedner, N.-A. Dreier, R. Engwer, Ch. Fritze, C. Gr¨ aser, Ch. Gr¨ uninger, D. Kempf, R. Kl¨ ofkorn, M. Ohlberger, and O. Sander. The Dune framework: Basic concepts and recent developments.CAMWA, 81:75–112, 2021

    work page 2021

  67. [67]

    Dedner and R

    A. Dedner and R. Kl¨ ofkorn. Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method.Commun. Appl. Math. Comput., 2021

    work page 2021

  68. [68]

    Nerf: Representing scenes as neural radiance fields for view synthesis.Communications of the ACM, 65(1):99–106, 2021

    Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis.Communications of the ACM, 65(1):99–106, 2021

    work page 2021

  69. [69]

    MIT press Cambridge, 2016

    Ian Goodfellow, Yoshua Bengio, Aaron Courville, and Yoshua Bengio.Deep learning, volume 1. MIT press Cambridge, 2016

    work page 2016

  70. [70]

    Sub-millisecond 4d x-ray tomography achieved with a multibeam x-ray imaging system.Applied Physics Express, 16(7):072001, 2023

    Xiaoyu Liang, Wolfgang Voegeli, Hiroyuki Kudo, Etsuo Arakawa, Tetsuroh Shirasawa, Kentaro Kajiwara, Tadashi Abukawa, and Wataru Yashiro. Sub-millisecond 4d x-ray tomography achieved with a multibeam x-ray imaging system.Applied Physics Express, 16(7):072001, 2023

    work page 2023

  71. [71]

    Dy- namic sparse x-ray nanotomography reveals ionomer hydration mechanism in polymer electrolyte fuel-cell catalyst.Science Advances, 10(41):eadp3346, 2024

    Zirui Gao, Christian Appel, Mirko Holler, Katharina Jeschonek, Kai Brunnengr¨ aber, Bastian JM Etzold, Michal Kronenberg, Marco Stampanoni, Johannes Ihli, and Manuel Guizar-Sicairos. Dy- namic sparse x-ray nanotomography reveals ionomer hydration mechanism in polymer electrolyte fuel-cell catalyst.Science Advances, 10(41):eadp3346, 2024

    work page 2024

  72. [72]

    Synchrotron x-ray multi-projection imaging for multiphase flow.arXiv preprint arXiv:2412.09368, 2024

    Tomas Ros´ en, Zisheng Yao, Jonas Tejbo, Patrick Wegele, Julia K Rogalinski, Frida Nilsson, Kannara Mom, Zhe Hu, Samuel A McDonald, Kim Nyg˚ ard, et al. Synchrotron x-ray multi-projection imaging for multiphase flow.arXiv preprint arXiv:2412.09368, 2024. 14 - Supplementary Material -1 An evaluation framework for sparse 4D (3D + time) imaging2 reconstructi...

    work page arXiv 2024