pith. sign in

arxiv: 2606.18058 · v1 · pith:IOARMXLGnew · submitted 2026-06-16 · 📡 eess.IV · q-bio.QM

Multiscale reconstruction of protein conformations from cryo-EM images

David Y. W. Thong , Ozan \"Oktem , Joakim And\'en This is my paper

Pith reviewed 2026-06-26 22:17 UTC · model grok-4.3

classification 📡 eess.IV q-bio.QM
keywords cryo-EMprotein structure recoverymultiscale algorithmatomic modelbackbone representationimage reconstructionTEM
0
0 comments X

The pith

A multiscale algorithm using explicit protein backbone representation recovers atomic structures from noisy cryo-EM images.

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

The paper presents a multiscale algorithm that directly recovers the atomic model of a protein from single-particle cryo-EM data. It relies on an explicit backbone representation defined by bonds, torsion angles, and bond angles to inject strong prior information into the recovery process. This yields state-of-the-art accuracy on high-noise, low-contrast images and remains robust when the image formation model is misspecified. Experiments on three simulated datasets show that the multiscale approach improves root-mean-square deviation and template modeling scores relative to ground truth. The method also tends to prioritize larger-scale structures, which helps optimization avoid poor local minima.

Core claim

We present a novel multiscale algorithm for directly recovering the atomic model structure of a protein from single-particle cryo-EM data. Our algorithm is able to estimate protein structures to state-of-the-art accuracy for high-noise and low-contrast data. It is also robust to misspecifications in the TEM image formation model. These desirable properties are primarily due to the use of an explicit representation of the protein backbone in terms of bonds, torsion angles and bond angles, which supplies rich prior information to the structure recovery process. We apply our method on three protein cryo-EM datasets, generated using an electron microscope digital twin, and show that using a mult

What carries the argument

multiscale optimization guided by an explicit protein backbone model expressed through bonds, torsion angles, and bond angles

If this is right

  • The algorithm achieves state-of-the-art accuracy on high-noise and low-contrast cryo-EM data.
  • Performance remains stable even when the TEM image formation model is misspecified.
  • Multiscale processing improves RMSD and TM scores relative to non-multiscale baselines on the tested datasets.
  • Larger-scale structures are recovered first, lowering the chance of convergence to bad local minima.
  • The method works directly on single-particle cryo-EM data to produce atomic models.

Where Pith is reading between the lines

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

  • The backbone prior could be combined with other geometric constraints to handle even lower signal-to-noise ratios.
  • Similar multiscale strategies might transfer to related inverse problems such as tomography of non-protein macromolecules.
  • If the backbone representation proves sufficient on real experimental images, it would reduce reliance on high-resolution reference maps during initial modeling.

Load-bearing premise

The explicit representation of the protein backbone in terms of bonds, torsion angles and bond angles supplies rich prior information to the structure recovery process that is sufficient to guide multiscale optimization away from bad local minima.

What would settle it

Running the same three simulated datasets through the algorithm both with and without the multiscale schedule and comparing the resulting RMSD and TM scores to ground truth would show whether the reported gains are due to the multiscale strategy.

Figures

Figures reproduced from arXiv: 2606.18058 by David Y. W. Thong, Joakim And\'en, Ozan \"Oktem.

Figure 1
Figure 1. Figure 1: Diagram of a section of a protein backbone. The section is a polypep [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: An iterative refinement approach, where optimisation is performed on a coarsened representation, and is repeatedly refined at increasing levels of detail. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example images generated from cryo-EM simulator Parakeet for the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualisations for the 4AKE dataset. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Example particle images from the BPTI and 5VZ0 datasets. The bar [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Visualisations for the BPTI dataset. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Visualisations for the 5VZ0 dataset. Top row: template and target conformation visualisation (left) and fitted backbone structure (right). Bottom row: [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Plots of 2D slices of the loss surface along the first two principal [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: Plots of 2D slices of the loss surface on the same planes, at the same [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

We present a novel multiscale algorithm for directly recovering the atomic model structure of a protein from single-particle cryo-EM data. Our algorithm is able to estimate protein structures to state-of-the-art accuracy for high-noise and low-contrast data. It is also robust to misspecifications in the TEM image formation model. These desirable properties are primarily due to the use of an explicit representation of the protein backbone in terms of bonds, torsion angles and bond angles, which supplies rich prior information to the structure recovery process. We apply our method on three protein cryo-EM datasets, generated using an electron microscope digital twin, and show that using a multiscale approach yields an improvement of the root-mean-square deviation (RMSD) and template modelling (TM) scores with respect to the ground truth. Furthermore, there is evidence that larger-scale structures are being prioritised with the multiscale algorithm, which reduces the possibility of convergence to bad local minima.

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

3 major / 0 minor

Summary. The paper presents a multiscale algorithm for directly recovering atomic protein structures from single-particle cryo-EM data. It uses an explicit backbone representation parameterized by bonds, torsion angles, and bond angles to supply structural priors, claims state-of-the-art accuracy on high-noise/low-contrast data and robustness to TEM image-formation misspecifications, and reports RMSD/TM-score improvements on three simulated datasets generated by an electron-microscope digital twin, attributing gains to the multiscale strategy and backbone model.

Significance. If validated beyond the simulator, the explicit geometric backbone prior combined with multiscale optimization could provide a useful route to better convergence in low-SNR cryo-EM reconstruction. The approach is distinguished by its direct use of bond/torsion constraints rather than implicit density-based methods, but the current evidence base is confined to internal digital-twin experiments.

major comments (3)
  1. [Abstract / Experiments] Abstract and Experiments section: the reported RMSD and TM-score improvements are stated without numerical values, error bars, baseline comparisons, or ablation studies, preventing assessment of whether the multiscale backbone method actually reaches the claimed state-of-the-art accuracy.
  2. [Abstract / Experiments] Abstract and data-generation description: all robustness claims to TEM-model misspecifications rest on tests performed inside the same digital twin used to synthesize the three datasets; this leaves real-world effects (detector response, beam-induced motion, unknown aberrations, conformational heterogeneity outside the backbone parametrization) unexamined and makes the generalization claim load-bearing but unsupported.
  3. [Abstract] Abstract: the central attribution of performance gains to the explicit backbone prior and multiscale optimization is supported only by the three simulated cases; no additional controls, real-data tests, or analysis of local-minima avoidance are provided to substantiate that the prior is sufficient to steer optimization away from bad minima on experimental micrographs.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract / Experiments] Abstract and Experiments section: the reported RMSD and TM-score improvements are stated without numerical values, error bars, baseline comparisons, or ablation studies, preventing assessment of whether the multiscale backbone method actually reaches the claimed state-of-the-art accuracy.

    Authors: We agree that explicit numerical values, error bars, baseline comparisons, and ablation studies are needed for proper assessment. The experiments section reports the improvements but we will revise both the abstract and experiments to include the specific RMSD and TM-score values with statistics, direct baseline comparisons, and ablation results demonstrating the multiscale contribution. revision: yes

  2. Referee: [Abstract / Experiments] Abstract and data-generation description: all robustness claims to TEM-model misspecifications rest on tests performed inside the same digital twin used to synthesize the three datasets; this leaves real-world effects (detector response, beam-induced motion, unknown aberrations, conformational heterogeneity outside the backbone parametrization) unexamined and makes the generalization claim load-bearing but unsupported.

    Authors: The robustness tests were performed inside the digital twin to enable controlled evaluation of image-formation misspecifications. We acknowledge that this does not address all real-world effects such as beam-induced motion or conformational heterogeneity. In revision we will temper the generalization language in the abstract and add an explicit limitations discussion on the simulator's scope. revision: partial

  3. Referee: [Abstract] Abstract: the central attribution of performance gains to the explicit backbone prior and multiscale optimization is supported only by the three simulated cases; no additional controls, real-data tests, or analysis of local-minima avoidance are provided to substantiate that the prior is sufficient to steer optimization away from bad minima on experimental micrographs.

    Authors: The attribution rests on the three simulated datasets and the observed prioritization of larger-scale structures. We will add analysis of optimization trajectories to illustrate local-minima behavior in the revision. Real-data tests with unknown ground truth lie outside the current scope, which focuses on quantitative evaluation against known atomic models. revision: partial

standing simulated objections not resolved
  • Validation on real (non-simulated) experimental cryo-EM data

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper describes a multiscale optimization algorithm that uses an explicit backbone parametrization (bonds, torsion angles, bond angles) as prior information to recover protein structures from cryo-EM images. No equations, parameter-fitting steps, or self-citations are presented in the provided text that would reduce the reported RMSD/TM improvements or robustness claims to quantities defined by the same fitted parameters or by construction. The central claims rest on empirical results from simulated data rather than any self-referential derivation, making the algorithm's logic self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated beyond the domain assumption of backbone geometry.

axioms (1)
  • domain assumption Protein backbone geometry (fixed bonds, variable torsion and bond angles) supplies sufficient prior information to improve reconstruction from noisy cryo-EM data.
    Invoked when attributing performance gains to the explicit backbone representation.

pith-pipeline@v0.9.1-grok · 5697 in / 1238 out tokens · 34355 ms · 2026-06-26T22:17:04.098783+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

293 extracted references · 136 canonical work pages · 5 internal anchors

  1. [1]

    Proceedings of the 33rd

    Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and Köpf, Andreas and Yang, Edward and DeVito, Zach and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu and B...

  2. [2]

    , month = jul, year =

    Zhong, Ellen and Lerer, Adam and Davis, Joey and Berger, B. , month = jul, year =. Exploring generative atomic models in cryo-

  3. [3]

    Jamali, Kiarash and Kimanius, Dari and Scheres, Sjors HW , month = feb, year =. A

  4. [4]

    Gupta, Harshit and Phan, Thong Huy and Yoo, Jaejun and Unser, Michael , month = jul, year =. Multi-. Computer

  5. [6]

    Advances in neural information processing systems , author =

    Amortized. Advances in neural information processing systems , author =. 2022 , pmid =

    2022

  6. [7]

    2021 , note =

    Nature Methods , author =. 2021 , note =. doi:10.1038/s41592-020-01049-4 , abstract =

    work page doi:10.1038/s41592-020-01049-4 2021

  7. [8]

    Instances as queries,

    Zhong, Ellen and Lerer, Adam and Davis, Joseph H. and Berger, Bonnie , month = oct, year =. 2021. doi:10.1109/ICCV48922.2021.00403 , abstract =

    work page doi:10.1109/iccv48922.2021.00403 2021

  8. [9]

    arXiv preprint , author =

    Inferring a. arXiv preprint , author =

  9. [10]

    The FEBS Journal , author =

    Cryo-electron microscopy – a primer for the non-microscopist , volume =. The FEBS Journal , author =. 2013 , keywords =. doi:10.1111/febs.12078 , abstract =

    work page doi:10.1111/febs.12078 2013

  10. [11]

    Acta Crystallographica

    Macromolecular structure determination using. Acta Crystallographica. Section D, Structural Biology , author =. 2019 , pmid =. doi:10.1107/S2059798319011471 , abstract =

    work page doi:10.1107/s2059798319011471 2019

  11. [12]

    2021 , keywords =

    IEEE Transactions on Computational Imaging , author =. 2021 , keywords =. doi:10.1109/TCI.2021.3096491 , abstract =

    work page doi:10.1109/tci.2021.3096491 2021

  12. [13]

    International Conference on Information Fusion , author =

    A look at. International Conference on Information Fusion , author =. 2011 , pages =

    2011

  13. [14]

    Beckstein, Oliver and Seyler, Sean L. and. Simulated trajectory ensembles for the closed-to-open transition of adenylate kinase from. 2018 , keywords =. doi:10.6084/M9.FIGSHARE.7165306.V2 , abstract =

    work page doi:10.6084/m9.figshare.7165306.v2 2018

  14. [15]

    Acta Crystallographica Section D: Structural Biology , author =

    Real-space refinement in. Acta Crystallographica Section D: Structural Biology , author =. 2018 , pages =. doi:10.1107/S2059798318006551 , abstract =

    work page doi:10.1107/s2059798318006551 2018

  15. [16]

    2010 , pages =

    Acta Crystallographica Section D Biological Crystallography , author =. 2010 , pages =. doi:10.1107/S0907444909052925 , abstract =

    work page doi:10.1107/s0907444909052925 2010

  16. [17]

    bioRxiv preprint , publisher =

    Ducrocq, Gabriel and Grunewald, Lukas and Westenhoff, Sebastian and Lindsten, Fredrik , month = jun, year =. bioRxiv preprint , publisher =. doi:10.1101/2024.06.19.599686 , abstract =

    work page doi:10.1101/2024.06.19.599686 2024

  17. [18]

    Ultramicroscopy , author =

    Use of multivariate statistics in analysing the images of biological macromolecules , volume =. Ultramicroscopy , author =. 1981 , pages =. doi:10.1016/0304-3991(81)90059-0 , language =

    work page doi:10.1016/0304-3991(81)90059-0 1981

  18. [19]

    arXiv preprint , author =

    Protein. arXiv preprint , author =

  19. [20]

    SIAM Journal on Imaging Sciences , author =

    Structural. SIAM Journal on Imaging Sciences , author =. 2018 , pages =. doi:10.1137/17M1153509 , language =

    work page doi:10.1137/17m1153509 2018

  20. [21]

    Inverse Problems , author =

    Cryo-. Inverse Problems , author =. 2020 , pages =. doi:10.1088/1361-6420/ab4f55 , abstract =

    work page doi:10.1088/1361-6420/ab4f55 2020

  21. [22]

    Inverse Problems , author =

    Spectral decomposition of atomic structures in heterogeneous cryo-. Inverse Problems , author =. 2023 , pages =. doi:10.1088/1361-6420/acb2ba , abstract =

    work page doi:10.1088/1361-6420/acb2ba 2023

  22. [23]

    SIAM Journal on Imaging Sciences , author =

    Regularizing. SIAM Journal on Imaging Sciences , author =. 2023 , pages =. doi:10.1137/22M1520773 , language =

    work page doi:10.1137/22m1520773 2023

  23. [24]

    Manuscript in preparation , author =

    Multiscale reconstruction of protein conformations from cryo-. Manuscript in preparation , author =

  24. [25]

    and Shekhar, M

    Dashti, A. and Shekhar, M. S. and Hail, D. Ben and Mashayekhi, G. and Schwander, P. and Georges, A. des and Frank, J. and Singharoy, A. and Ourmazd, A. , month = jan, year =. Functional. bioRxiv preprint , publisher =. doi:10.1101/291922 , abstract =

    work page doi:10.1101/291922

  25. [26]

    2024 , pages =

    Nature Methods , author =. 2024 , pages =. doi:10.1038/s41592-024-02486-1 , language =

    work page doi:10.1038/s41592-024-02486-1 2024

  26. [27]

    Sigworth, Fred , year =

  27. [28]

    Kirkland, E. J. , year =. Advanced computing in electron microscopy , publisher =

  28. [29]

    Nature Protocols , author =

    I-. Nature Protocols , author =. 2010 , pages =. doi:10.1038/nprot.2010.5 , language =

    work page doi:10.1038/nprot.2010.5 2010

  29. [30]

    Proteins: Structure, Function, and Bioinformatics , author =

    Scoring function for automated assessment of protein structure template quality , volume =. Proteins: Structure, Function, and Bioinformatics , author =. 2004 , pages =. doi:10.1002/prot.20264 , abstract =

    work page doi:10.1002/prot.20264 2004

  30. [31]

    Acta Crystallographica Section D Biological Crystallography , author =

    The. Acta Crystallographica Section D Biological Crystallography , author =. 2006 , pages =. doi:10.1107/S0907444906022116 , number =

    work page doi:10.1107/s0907444906022116 2006

  31. [32]

    Acta Crystallographica Section D Biological Crystallography , author =

    Features and development of. Acta Crystallographica Section D Biological Crystallography , author =. 2010 , pages =. doi:10.1107/S0907444910007493 , abstract =

    work page doi:10.1107/s0907444910007493 2010

  32. [33]

    2023 , pages =

    Protein Science , author =. 2023 , pages =. doi:10.1002/pro.4792 , abstract =

    work page doi:10.1002/pro.4792 2023

  33. [34]

    2024 , pages =

    Nucleic Acids Research , author =. 2024 , pages =. doi:10.1093/nar/gkad1084 , abstract =

    work page doi:10.1093/nar/gkad1084 2024

  34. [35]

    Lindeberg, Tony , year =. Scale-. Wiley. doi:10.1002/9780470050118.ecse609 , note =

    work page doi:10.1002/9780470050118.ecse609

  35. [36]

    and Burt, P

    Adelson, E. and Burt, P. and Anderson, C. and Ogden, J. M. and Bergen, J. , month = nov, year =

  36. [37]

    Peng Li, Tega B

    Kirkland, Earl J. , year =. Advanced. doi:10.1007/978-1-4419-6533-2 , keywords =

    work page doi:10.1007/978-1-4419-6533-2

  37. [38]

    Chemical Reviews , author =

    Fragmentation. Chemical Reviews , author =. 2012 , note =. doi:10.1021/cr200093j , number =

    work page doi:10.1021/cr200093j 2012

  38. [39]

    Physical Review E , author =

    Discrete. Physical Review E , author =. 2011 , note =. doi:10.1103/PhysRevE.83.061908 , abstract =

    work page doi:10.1103/physreve.83.061908 2011

  39. [40]

    Methods in Molecular Biology (Clifton, N.J.) , author =

    Methods of protein structure comparison , volume =. Methods in Molecular Biology (Clifton, N.J.) , author =. 2012 , pmid =. doi:10.1007/978-1-61779-588-6_10 , abstract =

    work page doi:10.1007/978-1-61779-588-6_10 2012

  40. [41]

    PLOS Computational Biology , author =

    Path. PLOS Computational Biology , author =. 2015 , note =. doi:10.1371/journal.pcbi.1004568 , abstract =

    work page doi:10.1371/journal.pcbi.1004568 2015

  41. [42]

    2015 , keywords =

    Ultramicroscopy , author =. 2015 , keywords =. doi:10.1016/j.ultramic.2015.04.016 , abstract =

    work page doi:10.1016/j.ultramic.2015.04.016 2015

  42. [43]

    Open Biology , author =

    Parakeet: a digital twin software pipeline to assess the impact of experimental parameters on tomographic reconstructions for cryo-electron tomography , volume =. Open Biology , author =. 2021 , note =. doi:10.1098/rsob.210160 , abstract =

    work page doi:10.1098/rsob.210160 2021

  43. [44]

    2024 , note =

    Nature Methods , author =. 2024 , note =. doi:10.1038/s41592-023-02099-0 , abstract =

    work page doi:10.1038/s41592-023-02099-0 2024

  44. [45]

    IEEE Journal of Selected Topics in Signal Processing , author =

    Coarse-. IEEE Journal of Selected Topics in Signal Processing , author =. 2016 , note =. doi:10.1109/JSTSP.2015.2489186 , abstract =

    work page doi:10.1109/jstsp.2015.2489186 2016

  45. [46]

    Information and Inference: A Journal of the IMA , author =

    Sketching for large-scale learning of mixture models , volume =. Information and Inference: A Journal of the IMA , author =. 2018 , pages =. doi:10.1093/imaiai/iax015 , abstract =

    work page doi:10.1093/imaiai/iax015 2018

  46. [47]

    Gaussian mixture reduction via clustering , author =

  47. [48]

    and Plataniotis, K

    Assa, A. and Plataniotis, K. , year =. Wasserstein-. doi:10.1109/LSP.2018.2865829 , journal =

    work page doi:10.1109/lsp.2018.2865829 2018

  48. [49]

    Runnalls, A. R. , year =. Kullback-. doi:10.1109/TAES.2007.4383588 , journal =

    work page doi:10.1109/taes.2007.4383588 2007

  49. [50]

    Gaussian

    Zhang, Qiong and Zhang, Archer Gong and Chen, Jiahua , year =. Gaussian. doi:10.1109/TIT.2023.3323346 , journal =

    work page doi:10.1109/tit.2023.3323346 2023

  50. [51]

    2023 , url =

    Sajedi, A. and Lawryshyn, Y. and Plataniotis, K. , year =. A. doi:10.1109/ICASSP49357.2023.10096094 , journal =

    work page doi:10.1109/icassp49357.2023.10096094 2023

  51. [52]

    eLife , author =

    Characterisation of molecular motions in cryo-. eLife , author =. 2018 , note =. doi:10.7554/eLife.36861 , abstract =

    work page doi:10.7554/elife.36861 2018

  52. [53]

    Graphical Models and Image Processing , author =

    Three-. Graphical Models and Image Processing , author =. 1997 , pages =. doi:10.1006/gmip.1997.0420 , abstract =

    work page doi:10.1006/gmip.1997.0420 1997

  53. [54]

    Journal of Molecular Biology , author =

    Integrating. Journal of Molecular Biology , author =. 2023 , keywords =. doi:10.1016/j.jmb.2023.168014 , abstract =

    work page doi:10.1016/j.jmb.2023.168014 2023

  54. [55]

    Acta Crystallographica Section D: Structural Biology , author =

    Protein identification from electron cryomicroscopy maps by automated model building and side-chain matching , volume =. Acta Crystallographica Section D: Structural Biology , author =. 2021 , note =. doi:10.1107/S2059798321001765 , abstract =

    work page doi:10.1107/s2059798321001765 2021

  55. [56]

    2022 , note =

    Nature Methods , author =. 2022 , note =. doi:10.1038/s41592-021-01389-9 , abstract =

    work page doi:10.1038/s41592-021-01389-9 2022

  56. [57]

    Nature , author =

    Automated model building and protein identification in cryo-. Nature , author =. 2024 , note =. doi:10.1038/s41586-024-07215-4 , abstract =

    work page doi:10.1038/s41586-024-07215-4 2024

  57. [58]

    Acta Crystallographica

    Iterative model building, structure refinement and density modification with the. Acta Crystallographica. Section D, Biological Crystallography , author =. 2008 , pmid =. doi:10.1107/S090744490705024X , abstract =

    work page doi:10.1107/s090744490705024x 2008

  58. [59]

    Visualizing the Loss Landscape of Neural Nets

    Li, Hao and Xu, Zheng and Taylor, Gavin and Studer, Christoph and Goldstein, Tom , year =. Visualizing the. doi:10.48550/ARXIV.1712.09913 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1712.09913

  59. [60]

    Nature , author =

    Structures of α-synuclein filaments from human brains with. Nature , author =. 2022 , pmid =. doi:10.1038/s41586-022-05319-3 , abstract =

    work page doi:10.1038/s41586-022-05319-3 2022

  60. [61]

    Micromachines , author =

    Novel. Micromachines , author =. 2023 , pages =. doi:10.3390/mi14091674 , abstract =

    work page doi:10.3390/mi14091674 2023

  61. [62]

    2024 , note =

    Nature Methods , author =. 2024 , note =. doi:10.1038/s41592-024-02377-5 , abstract =

    work page doi:10.1038/s41592-024-02377-5 2024

  62. [63]

    Journal of Structural Biology , author =

    Fast multiscale reconstruction for. Journal of Structural Biology , author =. 2018 , keywords =. doi:10.1016/j.jsb.2018.09.008 , abstract =

    work page doi:10.1016/j.jsb.2018.09.008 2018

  63. [64]

    Journal of Structural Biology , author =

    Image formation modeling in cryo-electron microscopy , volume =. Journal of Structural Biology , author =. 2013 , keywords =. doi:10.1016/j.jsb.2013.05.008 , abstract =

    work page doi:10.1016/j.jsb.2013.05.008 2013

  64. [65]

    doi:10.1101/2023.10.31.564872 , abstract =

    Li, Yilai and Zhou, Yi and Yuan, Jing and Ye, Fei and Gu, Quanquan , month = nov, year =. doi:10.1101/2023.10.31.564872 , abstract =

    work page doi:10.1101/2023.10.31.564872 2023

  65. [66]

    Nature Methods , author =

    Improving resolution and resolvability of single-particle. Nature Methods , author =. 2024 , note =. doi:10.1038/s41592-023-02082-9 , abstract =

    work page doi:10.1038/s41592-023-02082-9 2024

  66. [67]

    Molecular biology of the cell

  67. [68]

    Nashed, Youssef S. G. and Poitevin, Frederic and Gupta, Harshit and Woollard, Geoffrey and Kagan, Michael and Yoon, Chun Hong and Ratner, Daniel , month = oct, year =. 2021. doi:10.1109/ICCVW54120.2021.00452 , urldate =

    work page doi:10.1109/iccvw54120.2021.00452 2021

  68. [69]

    Computer

    Levy, Axel and Poitevin, Frédéric and Martel, Julien and Nashed, Youssef and Peck, Ariana and Miolane, Nina and Ratner, Daniel and Dunne, Mike and Wetzstein, Gordon , month = oct, year =. Computer. doi:10.1007/978-3-031-19803-8_32 , abstract =

    work page doi:10.1007/978-3-031-19803-8_32

  69. [70]

    IEEE Transactions on Neural Networks and Learning Systems , author =

    Machine. IEEE Transactions on Neural Networks and Learning Systems , author =. 2022 , note =. doi:10.1109/TNNLS.2021.3131325 , abstract =

    work page doi:10.1109/tnnls.2021.3131325 2022

  70. [71]

    2021 , keywords =

    Matter , author =. 2021 , keywords =. doi:10.1016/j.matt.2021.09.004 , abstract =

    work page doi:10.1016/j.matt.2021.09.004 2021

  71. [72]

    and Goncharov, A

    Vainshtein, B. and Goncharov, A. , month = apr, year =. Determination of the spatial orientation of arbitrarily arranged identical particles of unknown structure from their projections , url =

  72. [73]

    Ultramicroscopy , author =

    Angular reconstitution:. Ultramicroscopy , author =. 1987 , pages =. doi:10.1016/0304-3991(87)90078-7 , abstract =

    work page doi:10.1016/0304-3991(87)90078-7 1987

  73. [74]

    Analyzing

    Alberts, Bruce and Johnson, Alexander and Lewis, Julian and Raff, Martin and Roberts, Keith and Walter, Peter , year =. Analyzing. Molecular

  74. [75]

    Journal of Structural Biology , author =

    Deep generative modeling for volume reconstruction in cryo-electron microscopy , volume =. Journal of Structural Biology , author =. 2022 , pages =. doi:10.1016/j.jsb.2022.107920 , language =

    work page doi:10.1016/j.jsb.2022.107920 2022

  75. [76]

    IEEE Signal Processing Magazine , author =

    Single-. IEEE Signal Processing Magazine , author =. 2020 , pages =. doi:10.1109/MSP.2019.2957822 , number =

    work page doi:10.1109/msp.2019.2957822 2020

  76. [77]

    Ghanem, Karam and Bzdok, Danilo , month = feb, year =. The. doi:10.48550/arXiv.2402.13369 , abstract =

    work page doi:10.48550/arxiv.2402.13369

  77. [78]

    , month = feb, year =

    Song, Yang and Kingma, Diederik P. , month = feb, year =. How to

  78. [79]

    Chang, Ziyi and Koulieris, George Alex and Shum, Hubert P. H. , month = oct, year =. On the

  79. [80]

    https://arxiv.org/pdf/2306.04542 , url =

    arXiv

  80. [81]

    Score-Based Generative Modeling through Stochastic Differential Equations

    Song, Yang and Sohl-Dickstein, Jascha and Kingma, Diederik P. and Kumar, Abhishek and Ermon, Stefano and Poole, Ben , year =. Score-. doi:10.48550/ARXIV.2011.13456 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2011.13456 2011

Showing first 80 references.