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Structural variability from noisy tomographic projections. (English) Zbl 1401.92117

MSC:
92C55 Biomedical imaging and signal processing
68U10 Computing methodologies for image processing
44A12 Radon transform
65R32 Numerical methods for inverse problems for integral equations
62G05 Nonparametric estimation
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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[1] G. S. Ammar and W. B. Gragg, The generalized Schur algorithm for the superfast solution of Toeplitz systems, in Rational Approximation and Its Applications in Mathematics and Physics, J. Gilewicz, M. Pindor, and W. Siemaszko, eds., Lecture Notes in Math. 1237, Springer, New York, 1987, pp. 315–330, .
[2] A. Amunts, A. Brown, X.-c. Bai, J. L. Llácer, T. Hussain, P. Emsley, F. Long, G. Murshudov, S. H. W. Scheres, and V. Ramakrishnan, Structure of the yeast mitochondrial large ribosomal subunit, Science, 343 (2014), pp. 1485–1489, .
[3] J. Andén, E. Katsevich, and A. Singer, Covariance estimation using conjugate gradient for 3D classification in CRYO-EM, in Proceedings of ISBI, 2015, pp. 200–204, .
[4] J. Andén and A. Singer, Factor analysis for spectral estimation, in Proceedings of SampTA, 2017, pp. 169–173, .
[5] O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, UK, 1996. · Zbl 0845.65011
[6] A. Barnett, L. Greengard, A. Pataki, and M. Spivak, Rapid solution of the cryo-EM reconstruction problem by frequency marching, SIAM J. Imaging Sci., 10 (2017), pp. 1170–1195, . · Zbl 1380.92036
[7] W. T. Baxter, R. A. Grassucci, H. Gao, and J. Frank, Determination of signal-to-noise ratios and spectral SNRs in cryo-EM low-dose imaging of molecules, J. Struct. Biol., 166 (2009), pp. 126–132, .
[8] T. Bhamre, T. Zhang, and A. Singer, Anisotropic Twicing for Single Particle Reconstruction Using Autocorrelation Analysis, , 2017.
[9] R. H. Chan and M. K. Ng, Conjugate gradient methods for Toeplitz systems, SIAM Rev., 38 (1996), pp. 427–482, . · Zbl 0863.65013
[10] T. F. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 766–771, . · Zbl 0646.65042
[11] X. Cheng, Random Matrices in High-Dimensional Data Analysis, Ph.D. thesis, Princeton University, Princeton, NJ, 2013, .
[12] Y. Cheng, N. Grigorieff, P. Penczek, and T. Walz, A primer to single-particle cryo-electron microscopy, Cell, 161 (2015), pp. 438–449, .
[13] R. R. Coifman and S. Lafon, Diffusion maps, Appl. Comput. Harmon. Anal., 21 (2006), pp. 5–30, . · Zbl 1095.68094
[14] J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp., 19 (1965), pp. 297–301, . · Zbl 0127.09002
[15] A. Dashti, P. Schwander, R. Langlois, R. Fung, W. Li, A. Hosseinizadeh, H. Y. Liao, J. Pallesen, G. Sharma, V. A. Stupina, A. E. Simon, J. D. Dinman, J. Frank, and A. Ourmazd, Trajectories of the ribosome as a Brownian nanomachine, Proc. Natl. Acad. Sci. USA, 111 (2014), pp. 17492–17497, .
[16] C. Davis and W. M. Kahan, The rotation of eigenvectors by a perturbation. III, SIAM J. Numer. Anal., 7 (1970), pp. 1–46, . · Zbl 0198.47201
[17] A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B Stat. Methodol., 39 (1977), pp. 1–38, . · Zbl 0364.62022
[18] E. Dobriban, W. Leeb, and A. Singer, Optimal Prediction in the Linearly Transformed Spiked Model, , 2017.
[19] D. L. Donoho, M. Gavish, and I. M. Johnstone, Optimal Shrinkage of Eigenvalues in the Spiked Covariance Model, , 2013. · Zbl 1403.62099
[20] V. Druskin and L. Knizhnerman, Two polynomial methods of calculating functions of symmetric matrices, USSR Comput. Math. Math. Phys., 29 (1989), pp. 112–121, . · Zbl 0719.65035
[21] A. Dutt and V. Rokhlin, Fast Fourier transforms for nonequispaced data, SIAM J. Sci. Comput., 14 (1993), pp. 1368–1393, . · Zbl 0791.65108
[22] H. Erickson and A. Klug, Measurement and compensation of defocusing and aberrations by Fourier processing of electron micrographs, Philos. Trans. Roy. Soc. Ser. B, 261 (1971), pp. 105–118, .
[23] J. A. Fessler, S. Lee, V. T. Olafsson, H. R. Shi, and D. C. Noll, Toeplitz-based iterative image reconstruction for MRI with correction for magnetic field inhomogeneity, IEEE Trans. Signal Process., 53 (2005), pp. 3393–3402, . · Zbl 1370.94033
[24] J. Frank, Three-Dimensional Electron Microscopy of Macromolecular Assemblies, Academic Press, New York, 2006.
[25] M. Gavish and D. L. Donoho, Optimal shrinkage of singular values, IEEE Trans. Inform. Theory, 63 (2017), pp. 2137–2152, . · Zbl 1366.94100
[26] G. H. Golub and C. F. Van Loan, Matrix Computations, 4th ed., Johns Hopkins University Press, Baltimore, 2013. · Zbl 1268.65037
[27] L. Greengard and J.-Y. Lee, Accelerating the nonuniform fast Fourier transform, SIAM Rev., 46 (2004), pp. 443–454, . · Zbl 1064.65156
[28] N. Grigorieff, FREALIGN: High-resolution refinement of single particle structures, J. Struct. Biol., 157 (2007), pp. 117 – 125, .
[29] M. Guerquin-Kern, D. V. D. Ville, C. Vonesch, J.-C. Baritaux, K. P. Pruessmann, and M. Unser, Wavelet-regularized reconstruction for rapid MRI, in Proceedings of ISBI, IEEE, 2009, pp. 193–196, .
[30] G. Harauz and M. van Heel, Exact filters for general geometry three dimensional reconstruction, Optik, 73 (1986), pp. 146–156.
[31] G. T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, Springer, New York, 2009, . · Zbl 1280.92002
[32] M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand., 49 (1952), . · Zbl 0048.09901
[33] N. J. Higham, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, 2008, .
[34] P. Jain, P. Netrapalli, and S. Sanghavi, Low-rank matrix completion using alternating minimization, in Proceedings of STOC, ACM, 2013, pp. 665–674, . · Zbl 1293.65073
[35] Q. Jin, C. Sorzano, J. de la Rosa-Trevín, J. Bilbao-Castro, R. Nún͂ez-Ramírez, O. Llorca, F. Tama, and S. Jonić, Iterative elastic 3D-to-2D alignment method using normal modes for studying structural dynamics of large macromolecular complexes, Structure, 22 (2014), pp. 496–506, .
[36] I. M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist., 29 (2001), pp. 295–327, . · Zbl 1016.62078
[37] S. Jonić, Computational methods for analyzing conformational variability of macromolecular complexes from cryo-electron microscopy images, Curr. Opin. Struct. Biol., 43 (2017), pp. 114–121, .
[38] E. Katsevich, A. Katsevich, and A. Singer, Covariance matrix estimation for the cryo-EM heterogeneity problem, SIAM J. Imaging Sci., 8 (2015), pp. 126–185, . · Zbl 1362.92036
[39] M. Khoshouei, M. Radjainia, W. Baumeister, and R. Danev, Cryo-EM structure of haemoglobin at 3.2 \AA determined with the volta phase plate, Nat. Commun., 8 (2017), .
[40] D. Kimanius, B. O. Forsberg, S. H. Scheres, and E. Lindahl, Accelerated cryo-EM structure determination with parallelisation using GPUs in RELION-2, eLife, 5 (2016), .
[41] A. Klug and R. A. Crowther, Three-dimensional image reconstruction from the viewpoint of information theory, Nature, 238 (1972), pp. 435–440, .
[42] W. Kühlbrandt, The resolution revolution, Science, 343 (2014), pp. 1443–1444, .
[43] S. Kunis and D. Potts, Fast spherical Fourier algorithms, J. Comput. Appl. Math., 161 (2003), pp. 75–98, . · Zbl 1033.65123
[44] R. R. Lederman and A. Singer, A Representation Theory Perspective on Simultaneous Alignment and Classification, , 2016.
[45] R. R. Lederman and A. Singer, Continuously heterogeneous hyper-objects in cryo-EM and \(3\)-D movies of many temporal dimensions, submitted, 2017, .
[46] H. Liao and J. Frank, Classification by bootstrapping in single particle methods, in Proceedings of ISBI, IEEE, 2010, pp. 169–172, .
[47] H. Y. Liao, Y. Hashem, and J. Frank, Efficient estimation of three-dimensional covariance and its application in the analysis of heterogeneous samples in cryo-electron microscopy, Structure, 23 (2015), pp. 1129–1137, .
[48] M. Liao, E. Cao, D. Julius, and Y. Cheng, Structure of the TRPV1 ion channel determined by electron cryo-microscopy, Nature, 504 (2013), pp. 107–112, .
[49] W. Liu and J. Frank, Estimation of variance distribution in three-dimensional reconstruction. I. Theory, J. Opt. Soc. Am. A, 12 (1995), pp. 2615–2627, .
[50] S. Lloyd, Least squares quantization in PCM, IEEE Trans. Inform. Theory, 28 (1982), pp. 129–137, . · Zbl 0504.94015
[51] S. Mallat, A Wavelet Tour of Signal Processing, 3rd ed., Academic Press, New York, 2008. · Zbl 0998.94510
[52] V. A. Marčenko and L. A. Pastur, Distribution of eigenvalues for some sets of random matrices, Math. USSR Sb., 1 (1967), p. 457, .
[53] E. Michielssen and A. Boag, A multilevel matrix decomposition algorithm for analyzing scattering from large structures, IEEE Trans. Antennas Propag., 44 (1996), pp. 1086–1093, .
[54] J. L. Milne, M. J. Borgnia, A. Bartesaghi, E. E. Tran, L. A. Earl, D. M. Schauder, J. Lengyel, J. Pierson, A. Patwardhan, and S. Subramaniam, Cryo-electron microscopy–A primer for the non-microscopist, FEBS J., 280 (2013), pp. 28–45, .
[55] J. A. Mindell and N. Grigorieff, Accurate determination of local defocus and specimen tilt in electron microscopy, J. Struct. Biol., 142 (2003), pp. 334–347, .
[56] B. Musicus, Levinson and Fast Cholesky Algorithms for Toeplitz and Almost Toeplitz Matrices, Tech. Report 538, MIT Research Laboratory of Electronics, Cambridge, MA, 1988.
[57] F. Natterer, The Mathematics of Computerized Tomography, Classics in Appl. Math. 32, SIAM, Philadelphia, 2001, . · Zbl 0973.92020
[58] D. Paul, Asymptotics of sample eigenstructure for a large dimensional spiked covariance model, Statist. Sinica, 17 (2007), pp. 1617–1642, . · Zbl 1134.62029
[59] P. Penczek, M. Kimmel, and C. Spahn, Identifying conformational states of macromolecules by eigen-analysis of resampled cryo-EM images, Structure, 19 (2011), pp. 1582–1590, .
[60] P. A. Penczek, Variance in three-dimensional reconstructions from projections, in Proceedings of ISBI, 2002, pp. 749–752, .
[61] P. A. Penczek, Image restoration in cryo-electron microscopy, in Cryo-EM, Part B: 3-D Reconstruction, G. J. Jensen, ed., Methods Enzymol. 482, Academic Press, New York, 2010, pp. 35–72, .
[62] P. A. Penczek, J. Frank, and C. M. Spahn, A method of focused classification, based on the bootstrap 3D variance analysis, and its application to EF-G-dependent translocation, J. Struct. Biol., 154 (2006), pp. 184–194, .
[63] P. A. Penczek, C. Yang, J. Frank, and C. M. Spahn, Estimation of variance in single-particle reconstruction using the bootstrap technique, J. Struct. Biol., 154 (2006), pp. 168–183, .
[64] A. Punjani, J. L. Rubinstein, D. J. Fleet, and M. A. Brubaker, cryoSPARC: Algorithms for rapid unsupervised cryo-EM structure determination, Nat. Methods, 14 (2017), pp. 290–296, .
[65] J. Radon, Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten, Berichte Sächsishen Akad. Wissenschaft. Math. Phys. Klass, 69 (1917), pp. 262–277. · JFM 46.0436.02
[66] Y. Saad, Analysis of some Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 29 (1992), pp. 209–228, . · Zbl 0749.65030
[67] Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Philadelphia, 2003, . · Zbl 1031.65046
[68] S. Scheres, RELION: Implementation of a Bayesian approach to cryo-EM structure determination, J. Struct. Biol., 180 (2012), pp. 519–530, .
[69] S. H. Scheres, A Bayesian view on cryo-EM structure determination, J. Molecular Biol., 415 (2012), pp. 406–418, .
[70] J. Schur, Über potenzreihen, die im innern des einheitskreises beschränkt sind., J. Reine Angew. Math., 147 (1917), pp. 205–232. · JFM 46.0475.01
[71] M. Shatsky, R. Hall, E. Nogales, J. Malik, and S. Brenner, Automated multi-model reconstruction from single-particle electron microscopy data, J. Struct. Biol., 170 (2010), pp. 98–108, .
[72] J. Shi and J. Malik, Normalized cuts and image segmentation, IEEE Trans. Pattern Anal. Mach. Intell., 22 (2000), pp. 888–905, .
[73] Y. Shkolnisky and A. Singer, Viewing direction estimation in cryo-EM using synchronization, SIAM J. Imaging Sci., 5 (2012), pp. 1088–1110, . · Zbl 1254.92058
[74] F. J. Sigworth, A maximum-likelihood approach to single-particle image refinement, J. Struct. Biol., 122 (1998), pp. 328–339, .
[75] A. Singer, R. R. Coifman, F. J. Sigworth, D. W. Chester, and Y. Shkolnisky, Detecting consistent common lines in cryo-EM by voting, J. Struct. Biol., 169 (2010), pp. 312–322, .
[76] D. Slepian, Prolate spheroidal wave functions, Fourier analysis and uncertainty–IV: Extensions to many dimensions; generalized prolate spheroidal functions, Bell Syst. Tech. J., 43 (1964), pp. 3009–3057, . · Zbl 0184.08604
[77] G. Strang, A proposal for Toeplitz matrix calculations, Stud. Appl. Math., 74 (1986), pp. 171–176, . · Zbl 0621.65025
[78] H. D. Tagare, A. Kucukelbir, F. J. Sigworth, H. Wang, and M. Rao, Directly reconstructing principal components of heterogeneous particles from cryo-EM images, J. Struct. Biol., 191 (2015), pp. 245–262, .
[79] L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997.
[80] M. Tygert, Fast algorithms for spherical harmonic expansions, III, J. Comput. Phys., 229 (2010), pp. 6181–6192, . · Zbl 1201.65037
[81] E. E. Tyrtyshnikov, Optimal and superoptimal circulant preconditioners, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 459–473, . · Zbl 0774.65024
[82] M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, and A. Patwardhan, Single-particle electron cryo-microscopy: Towards atomic resolution, Q. Rev. Biophys., 33 (2000), pp. 307–369, .
[83] K. R. Vinothkumar and R. Henderson, Single particle electron cryomicroscopy: Trends, issues and future perspective, Q. Rev. Biophys., 49 (2016), .
[84] C. Vonesch, L. Wang, Y. Shkolnisky, and A. Singer, Fast wavelet-based single-particle reconstruction in cryo-EM, in Proceedings of ISBI, IEEE, 2011, pp. 1950–1953, .
[85] M. Vulović, R. B. Ravelli, L. J. van Vliet, A. J. Koster, I. Lazić, U. Lücken, H. Rullg\aard, O. Öktem, and B. Rieger, Image formation modeling in cryo-electron microscopy, J. Struct. Biol., 183 (2013), pp. 19–32, .
[86] R. Wade, A brief look at imaging and contrast transfer, Ultramicroscopy, 46 (1992), pp. 145–156, .
[87] F. T. A. W. Wajer and K. P. Pruessmann, Major speedup of reconstruction for sensitivity encoding with arbitrary trajectories, in Proceedings of ISMRM, 2001, p. 767.
[88] L. Wang, Y. Shkolnisky, and A. Singer, A Fourier-Based Approach for Iterative 3D Reconstruction from Cryo-EM Images, , 2013.
[89] L. Wang, A. Singer, and Z. Wen, Orientation determination of cryo-EM images using least unsquared deviations, SIAM J. Imaging Sci., 6 (2013), pp. 2450–2483, . · Zbl 1402.92449
[90] N. Xu, D. Veesler, P. C. Doerschuk, and J. E. Johnson, Allosteric effects in bacteriophage HK\(97\) procapsids revealed directly from covariance analysis of cryo EM data, J. Struct. Biol., 202 (2018), pp. 129–141, .
[91] K. Zhang, GCTF: Real-time CTF determination and correction, J. Struct. Biol., 193 (2016), pp. 1–12, .
[92] Z. Zhao and A. Singer, Fourier–Bessel rotational invariant eigenimages, J. Opt. Soc. Am. A, 30 (2013), pp. 871–877, .
[93] Z. Zhao and A. Singer, Rotationally invariant image representation for viewing direction classification in cryo-EM, J. Struct. Biol., 186 (2014), pp. 153–166, .
[94] Y. Zheng, Q. Wang, and P. C. Doerschuk, Three-dimensional reconstruction of the statistics of heterogeneous objects from a collection of one projection image of each object, J. Opt. Soc. Am. A, 29 (2012), pp. 959–970, .
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