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Maximum likelihood for high-noise group orbit estimation and single-particle cryo-EM
[article]
2021
arXiv
pre-print
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Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a low SNR regime, where samples are observed under random rotations ...
of cryo-EM as introduced by Bandeira, Blum-Smith, Kileel, Perry, Weed, and Wein. ...
We would like to thank Fred Sigworth for helpful discussions about cryo-EM, and for suggesting to us the hemoglobin example. ZF was supported in part by NSF DMS-1916198. ...
arXiv:2107.01305v1
fatcat:mxfmbmytirhcpj4zg5t2yavse4
Estimation of Orientation and Camera Parameters from Cryo-Electron Microscopy Images with Variational Autoencoders and Generative Adversarial Networks
[article]
2021
arXiv
pre-print
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2019 pre-print arXiv:1911.08121v1 fatcat:sj7o2tgmcraytoningj64ukssy
This analysis leads us to design an estimation method for orientation and camera parameters of single-particle cryo-EM images, together with an outliers detection procedure. ...
As such, it opens the door to geometric approaches for unsupervised estimations of orientations and camera parameters, making possible fast cryo-EM biomolecule reconstruction. ...
Acknowledgments We thank Khanh Dao Duc and TJ Lane for very helpful comments on an earlier draft of the manuscript, and Daniel Ratner and Cornelius Gati for stimulating discussions and support throughout ...
arXiv:1911.08121v2
fatcat:l2snznfj6bgoznvkbotzyx4c6y
Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities
[article]
2019
arXiv
pre-print
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Based on these abstractions, we discuss some recent intriguing results in the mathematical theory of cryo-EM, and delineate relations with group theory, invariant theory, and information theory. ...
Determining molecular structures requires a wide range of computational tools in a variety of fields, including signal processing, estimation and detection theory, high-dimensional statistics, convex and ...
ACKNOWLEDGMENT We thank the anonymous reviewers and the editor for their valuable comments and suggestions. ...
arXiv:1908.00574v2
fatcat:lwbbis37e5ctjngflw3opjl4sy
Mathematics for cryo-electron microscopy
[article]
2018
arXiv
pre-print
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Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. ...
This paper focuses on the mathematical principles underlying existing algorithms for structure determination using single particle cryo-EM. ...
There are two aspects that make single particle reconstruction (SPR) from cryo-EM more challenging compared to classical CT. ...
arXiv:1803.06714v1
fatcat:cg5a2zhwkjfmzeqj44lunrhspa
The generalized method of moments for multi-reference alignment
[article]
2021
arXiv
pre-print
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We begin by proving that the GMM estimator maintains its asymptotic optimality for statistical models with group symmetry, including MRA. ...
We also formulate the GMM to estimate a three-dimensional molecular structure using cryo-electron microscopy and present numerical results on simulated data. ...
GMM FOR CRYO-EM: A PROOF OF CONCEPT As aforementioned, the main motivation of this work stems from the task of reconstructing the 3-D structure of molecular structures using single-particle cryo-EM. ...
arXiv:2103.02215v2
fatcat:gwntrj32tfdopkkxzz3yok2d34
Dihedral multi-reference alignment
[article]
2022
arXiv
pre-print
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2021 pre-print arXiv:2107.05262v1 fatcat:ishp77p52ncyxnucex3oon7wem
This implies that the optimal estimation rate in the high noise regime is proportional to the square of the variance of the noise. ...
Based on tools from invariant theory and algebraic geometry, we also delineate conditions for unique orbit recovery for multi-reference alignment models over finite groups (namely, when the dihedral group ...
To estimate the signal in high noise levels, we also suggest maximizing the marginalized maximum likelihood using expectation-maximization (EM). ...
arXiv:2107.05262v2
fatcat:bmugkzqtr5ew5ppmu3l5eeseeq
Structural Analysis of Macromolecular Assemblies by Electron Microscopy
2011
Chemical Reviews
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Gohlke, and Stephen Fuller for providing figures, and Andrew Service and Anne-Cecile Maffat for help with manuscript preparation. ...
ACKNOWLEDGMENT We thank Joachim Frank, Richard Henderson, Ronald Milligan, and Peter Rosenthal for helpful comments on the manuscript, Dan Clare, Maud Dumoux, Richard Hayward, Maya Topf, Neil Ranson, Uli ...
Single-particle cryo-EM becomes very difficult when the particle is less than a few hundred kDa in mass. ...
doi:10.1021/cr100353t
pmid:21919528
pmcid:PMC3239172
fatcat:bx7j3f6dajalzitk63mgx3nxhq
Deep manifold learning reveals hidden dynamics of proteasome autoregulation
[article]
2021
arXiv
pre-print
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By using AlphaCryo4D to analyze a single experimental cryo-EM dataset, we identified 64 conformers of the substrate-bound human 26S proteasome, revealing conformational entanglement of two regulatory particles ...
Here we introduce a deep manifold learning framework, named AlphaCryo4D, which enables atomic-level cryogenic electron microscopy (cryo-EM) reconstructions of nonequilibrium conformational continuum and ...
Figure 1 . 1 Conceptual framework of AlphaCryo4D for 4D cryo-EM reconstruction. a, Schematic showing the major conceptual steps of single-particle cryo-EM data processing in AlphaCryo4D. b, Illustration ...
arXiv:2012.12854v2
fatcat:g3xx3xzfinbutgmkwcrjkyikga
Deep manifold learning reveals hidden dynamics of proteasome autoregulation
[article]
2020
bioRxiv
pre-print
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By using AlphaCryo4D to analyze a single experimental cryo-EM dataset, we identified 64 conformers of the substrate-bound human 26S proteasome, revealing conformational entanglement of two regulatory particles ...
Here we introduce a deep manifold learning framework, named AlphaCryo4D, which enables atomic-level cryogenic electron microscopy (cryo-EM) reconstructions of nonequilibrium conformational continuum and ...
Figure 1 . 1 Conceptual framework of AlphaCryo4D for 4D cryo-EM reconstruction. a,539 Schematic showing the major conceptual steps of single-particle cryo-EM data processing in540 AlphaCryo4D. b, Illustration ...
doi:10.1101/2020.12.22.423932
fatcat:txhdd7nborh35orefd4ovpoyrq
Multi-reference alignment in high dimensions: sample complexity and phase transition
[article]
2020
arXiv
pre-print
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Motivated by single-particle cryo-electron microscopy, we analyze the sample complexity of the problem in the high-dimensional regime L→∞. ...
Namely, the number of measurements required to achieve a desired accuracy ε approaches σ^2/ε for small ε; this is the sample complexity of estimating a signal in additive white Gaussian noise, which does ...
Therefore, we can only estimate the orbit of X under the group of circular shifts Z L . ...
arXiv:2007.11482v1
fatcat:ifqn22nwtbb5jd7ctp2t26mzge
Multireference Alignment is Easier with an Aperiodic Translation Distribution
[article]
2018
arXiv
pre-print
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In this work, using a generalization of the Chapman--Robbins bound for orbits and expansions of the χ^2 divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation ...
In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. ...
ACKNOWLEDGMENTS We would like to thank Afonso Bandeira, Nicolas Boumal, Joseph Kileel, Roy Lederman and Zhizhen Zhao for many insightful discussions. ...
arXiv:1710.02793v3
fatcat:pv6wbujrpzfz7eahzadubjr2ee
Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles
[article]
2019
arXiv
pre-print
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Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3-D structure of a molecule from several noisy 2-D projections images taken ...
For unknown, non-uniform distributions, we use non-convex optimization methods to solve for both the molecule and distribution. ...
The authors thank Nicolas Boumal, Peter Bürgisser, Eitan Levin, Dilano Saldin and Yoel Shkolnisky for stimulating conversations, and the anonymous referees for their valuable comments. ...
arXiv:1907.05377v2
fatcat:5hovat6mpbhadnevzdik6cl3fq
Likelihood landscape and maximum likelihood estimation for the discrete orbit recovery model
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2004.00041v2 fatcat:rwfl3lvehfextkvn3rucstqmdiOther Versions
We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. ...
We show that fundamental properties of the likelihood landscape depend on the signal-to-noise ratio and the group structure. ...
We would like to thank Roy Lederman for helpful conversations at the onset of this work. Z. F. was supported in part by NSF Grant DMS-1916198. Y. ...
arXiv:2004.00041v4
fatcat:jjoklj6rknfihhuzaot524hhje
Measuring image resolution in optical nanoscopy
2013
Nature Methods
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for assistance with experiments; and V. van Ravesteijn and P. Kruit for providing scanning electron microscope data. ...
We appreciate the thoughtful comments of T. reprints and permissions information is available online at http://www.nature. com/reprints/index.html. ...
It is centered on the FRC (or, equivalently, the spectral signal-to-noise ratio), which is commonly used in the field of cryo-electron microscopy (cryo-EM) to assess single-particle reconstructions of ...
doi:10.1038/nmeth.2448
pmid:23624665
pmcid:PMC4149789
fatcat:v3vyc77xk5bzfbfbf5ebi2ho2a
On random tomography with unobservable projection angles
2009
Annals of Statistics
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The problem arises in single particle electron microscopy, a powerful method that biophysicists employ to learn the structure of biological macromolecules. ...
projections in random and unobservable directions. ...
Finally, my thanks go to an Associate Editor and the referees for their thorough and constructive comments. ...
doi:10.1214/08-aos673
fatcat:ng3dsio4kncdjj7jcy7ybghhwq
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