E. Verbeke, M.A. Gilles, T. Bendory, A. Singer,  Self Fourier shell correlation: properties and application to cryo-ET, Communications Biology, 7:101 (2024). PMID: 38228756 PMCID: PMC10791666


M.A. Gilles, A. Singer,  A Bayesian Framework for Cryo-EM Heterogeneity Analysis using Regularized Covariance Estimation, bioRxiv (2023).

T. Bendory, Y. Khoo, J. Kileel, O. Mickelin, A. Singer,  Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms, Proceedings of the National Academy of Sciences, 120 (18) e2216507120 (2023). PMID: 37094135 PMCID: PMC10161091

N. F. Marshall, O. Mickelin, Y. Shi, A. Singer,  Fast Principal Component Analysis for Cryo-EM Images, Biological Imaging, 3, E2 (2023). PMID: 37645688 PMCID: PMC10465116

N. F. Marshall, O. Mickelin, A. Singer,  Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions, SIAM Journal on Scientific Computing, 45 (5), pp. A2431-A2457 (2023).

T. Bendory, N. Boumal, W. Leeb, E. Levin, A. Singer,  Toward single particle reconstruction without particle picking: Breaking the detection limit, SIAM Journal on Imaging Sciences, 16 (2), pp. 886-910 (2023).

T. Bendory, T.-Y. Lan, N.F. Marshall, I. Rukshin, A. Singer,  Multi-target detection with rotations, Inverse Problems and Imaging, 17 (2), pp. 362-380 (2023).



Y. Shi and A. Singer,  Ab-initio Contrast Estimation and Denoising of Cryo-EM Images, Computer Methods and Programs in Biomedicine, 224, pp. 107018 (2022). PMID: 35901641 PMCID: PMC9392052

M.A. Gilles and A. Singer,  A Molecular Prior Distribution for Bayesian Inference Based on Wilson Statistics, Computer Methods and Programs in Biomedicine, 221, pp. 106830 (2022). PMID: 35537297 PMCID: PMC9233040

S. Kreymer, A. Singer, T. Bendory,  An approximate expectation-maximization for two-dimensional multi-target detection, IEEE Signal Processing Letters, 29, pp. 1087-1091 (2022). PMID: 35601688 PMCID: PMC9119315

T. Bendory, O. Mickelin, A. Singer,  Sparse multi-reference alignment: sample complexity and computational hardness, ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Singapore, pp. 8977-8981 (2022).

T.-Y. Lan, N. Boumal, A. Singer,  Random Conical Tilt Reconstruction without Particle Picking in Cryo-electron Microscopy, Acta Crystallographica Section A: Foundations and Advances, 78 (4) (2022). PMID: 35781409 PMCID: PMC9252301



A. Singer,  Wilson Statistics: Derivation, Generalization, and Applications to Electron Cryomicroscopy, Acta Crystallographica Section A: Foundations and Advances, 77 (5), pp. 472-479 (2021). PMID: 34473100 PMCID: PMC8477642

A. Heimowitz, N. Sharon, A. Singer,  Centering noisy images with application to cryo-EM, SIAM Journal on Imaging Sciences, 14 (2), pp. 689-716 (2021). PMID: 35126803 PMCID: PMC8813033

T. Bendory, A. Jaffe, W. Leeb, N. Sharon, A. Singer,  Super-resolution multi-reference alignment, Information and Inference: A Journal of the IMA, 11 (2), pp. 533-555 (2021). PMID: 35966813 PMCID: PMC9374099



R. Rao, A. Moscovich, A. Singer,  Wasserstein K-Means for Clustering Tomographic Projections, NeurIPS 2020, Machine Learning for Structural Biology (MLSB) Workshop.

A. Singer and F.J. Sigworth,  Computational Methods for Single-Particle Cryo-EM, Annual Review of Biomedical Data Science, 3, pp. 163-190 (2020). PMID: 34485850 PMCID: PMC8412055

T. Bendory, A. Bartesaghi, A. Singer,  Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities, IEEE Signal Processing Magazine, 37 (2), pp. 58-76, 2020. PMID: 32395065 PMCID: PMC7213211

A. Heimowitz, J. Andén, A. Singer,  Bias and variance reduction and denoising for CTF Estimation, Ultramicroscopy, 212, 112950, 2020. PMID: 32151795 PMCID: PMC9930185

T.-Y. Lan, T. Bendory, N. Boumal, A. Singer,  Multi-target detection with an arbitrary spacing distribution, IEEE Transactions on Signal Processing, 68 (1), pp. 1589-1601 (2020). NIHMSID: NIHMS1578253 PMCID: PMC7977005

N. Zelesko, A. Moscovich, J. Kileel, A. Singer,  Earthmover-based manifold learning for analyzing molecular conformation spaces, 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI 2020), Iowa City, IA, USA, pp. 1715-1719 (2020).

C. Ma, T. Bendory, N. Boumal, F. Sigworth, A. Singer, Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction,  IEEE Transactions on Image Processing, 29 (1), pp. 1699-1710 (2020). PMID: 31613760

N. Sharon, J. Kileel, Y. Khoo, B. Landa, A. Singer,  Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles, Inverse Problems, 36 (4) p.044003, 2020.

A. S. Bandeira, Y. Chen, R. R. Lederman, A. Singer,  Non-Unique Games over Compact Groups and Orientation Estimation in Cryo-EM, Inverse Problems, 36 (6) p.064002, 2020. PMID: 38274355 PMCID: PMC10810340

R. R. Lederman, J. Andén, A. Singer,  Hyper-molecules: on the representation and recovery of dynamical structures for applications in flexible macro-molecules in cryo-EM, Inverse Problems, 36 (4) p.044005, 2020.

A. Moscovich, A. Halevi, J. Andén, A. Singer,  Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes, Inverse Problems, 36 (2) p.024003, 2020. PMID: 32394996 PMCID: PMC7213598

R. R. Lederman, A. Singer, A Representation Theory Perspective on Simultaneous Alignment and Classification,  Applied and Computational Harmonic Analysis, 49 (3), pp. 1001-1024 (2020).


T. Bendory, N. Boumal, W. Leeb, E. Levin, A. Singer,  Multi-target detection with application to cryo-electron microscopy, Inverse Problems, 35(10), p.104003, 2019.

G. Pragier, Y. Shkolnisky,  A common lines approach for ab-initio modeling of cyclically-symmetric molecules, Inverse Problems, 35(12), p.124005, 2019.

A. Perry, J. Weed, A. S. Bandeira, P. Rigollet, A. Singer, The sample complexity of multi-reference alignment,  SIAM Journal on Mathematics of Data Science, 1 (3), pp. 497-517 (2019).​

E. Abbe, T. Bendory, W. Leeb, J. Pereira, N. Sharon, A. Singer, Multireference Alignment is Easier with an Aperiodic Translation Distribution,  IEEE Transactions on Information Theory, 65 (6), pp. 3565-3584 (2019).



A. Singer,  Mathematics for cryo-electron microscopy, Proceedings of the International Congress of Mathematicians, 2018.

A. Heimowitz, J. Andén, A. Singer, APPLE Picker: Automatic Particle Picking, a Low-Effort Cryo-EM Framework, Journal of Structural Biology, 204(2), pp. 215-227, 2018. PMID: 30134153 [PubMed]  PMCID: PMC6183064.

J. Andén, A. Singer, Structural Variability from Noisy Tomographic ProjectionsSIAM Journal on Imaging Sciences, 11(2), pp. 1441-1492, 2018.​ PMID: 30555617 [PubMed] PMCID: PMC6294454.

E. Levin, T. Bendory, N. Boumal, J. Kileel, A. Singer, 3D ab initio modeling in cryo-EM by autocorrelation analysis, in IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018), pp. 1569-1573, 2018.

N. Boumal, T. Bendory, R. R. Lederman, A. Singer, Heterogeneous multireference alignment: a single pass approach, in IEEE 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1-6, 2018.  

T. Bendory, N. Boumal, C. Ma, Z. Zhao, A. Singer, Bispectrum Inversion with Application to Multireference AlignmentIEEE Transactions on Signal Processing, 66(4), pp. 1037-1050, 2018. PMID: 29805244 [PubMed] PMCID: PMC5966049.



T. Bhamre, T. Zhang, A. Singer, Anisotropic twicing for single particle reconstruction using autocorrelation analysis, arXiv preprint.

E. Abbe, J. Pereira, A. Singer, Sample Complexity of the Boolean Multireference Alignment ProblemIEEE International Symposium on Information Theory (ISIT), pp. 1316-1320, 2017. PMID: 29755834 [PubMed] PMCID: PMC5947970.

I. Greenberg, Y. Shkolnisky, Common Lines Modeling for Reference Free Ab-Initio Reconstruction in Cryo-EM, Journal of Structural Biology, 200(2), pp.106-117, 2017. PMID: 28943480.

B. Landa, Y. Shkolnisky, Steerable Principal Components for Space-Frequency Localized ImagesSIAM Journal on Imaging Sciences, 10(2), 508–534, 2017. PMID: 29081879 [PubMed] PMCID: PMC5659640.

T. Zhang, A. Singer, Disentangling Orthogonal MatricesLinear Algebra and Applications, 524, pp. 159-181 (2017). PMID: 29332952 [PubMed] PMCID: PMC5766317.

T. Bhamre, Z. Zhao, A. Singer, Mahalanobis Distance for Class Averaging of Cryo-EM Images2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017), Melbourne, VIC, pp. 654-658, 2017. PMID: 29081898 [PubMed] PMCID: PMC5657188.

J. Andén, A. Singer, Factor Analysis for Spectral EstimationSampling Theory and Applications (SampTA), 12th International Conference, pp. 169-173, 2017.  PMID: 30854520 [PubMed] PMCID: PMC6405211.



T. Bhamre, T. Zhang, A. Singer, Denoising and Covariance Estimation of Single Particle Cryo-EM Images, Journal of Structural Biology, 195 (1), pp. 72-81 (2016). PMID:27129418 [PubMed - in process]

G. Pragier, I. Greenberg, X. Cheng and Y. Shkolnisky, A Graph Partitioning Approach to Simultaneous Angular ReconstitutionIEEE Transactions on Computational Imaging, 2 (3), pp. 323-334 (2016). PMID: 28217720 [PubMed] PMCID: PMC5315492 

Z. Zhao, Y. Shkolnisky, A. Singer, Fast Steerable Principal Component AnalysisIEEE Transactions on Computational Imaging, 2 (1), pp. 1-12 (2016).​ PMID: 27570801 [PubMed] PMCID: PMC4996495​.



T. Bhamre, T. Zhang, A. Singer, Orthogonal Matrix Retrieval in Cryo-Electron Microscopy, in IEEE 12th International Symposium on Biomedical Imaging (ISBI 2015), pp. 1048-1052, 16-19 April 2015. PMID: 26677402 [PubMed] PMCID: PMC4678003

J. Andén, E. Katsevich, A. Singer, Covariance estimation using conjugate gradient for 3D classification in Cryo-EM, in IEEE 12th International Symposium on Biomedical Imaging (ISBI 2015), pp. 200-204, 16-19 April 2015. PMID: 26682015 [PubMed] PMCID: PMC4679407

E. Katsevich, A. Katsevich, A. Singer, Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem, SIAM Journal on Imaging Sciences, 8 (1), pp. 126-185 (2015). PMID: 25699132 [PubMed] PMCID: PMC4331039



Z. Zhao, A. Singer, Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM, Journal of Structural Biology, 186 (1), pp. 153-166 (2014). PMID: 24631969 [PubMed] PMCID: PMC4014198



L. Wang, A. Singer, Z. Wen, Orientation Determination from Cryo-EM images using Least Unsquared DeviationsSIAM Journal on Imaging Sciences, 6 (4), pp. 2450-2483 (2013). PMID:24683433 [PubMed] PMCID: PMC3966634.

Z. Zhao, A. Singer, Fourier-Bessel Rotational Invariant Eigenimages, The Journal of the Optical Society of America A, 30 (5), pp. 871-877 (2013). PMID: 23695317 [PubMed] PMCID: PMC3711886.

A. Singer, H.-T. Wu, Two-Dimensional tomography from noisy projections taken at unknown random directions, SIAM Journal on Imaging Sciences, 6 (1), pp. 136-175 (2013). PMID: 24563691 [PubMed] PMCID: PMC3929313



Y. Shkolnisky, A. Singer, Viewing Direction Estimation in Cryo-EM Using Synchronization, SIAM Journal on Imaging Sciences, 5 (3), pp. 1088-1110 (2012). PMID: 24363820 [PubMed] PMCID: PMC3868463.

A. Singer, H.-T. Wu, Vector Diffusion Maps and the Connection Laplacian, Communications on Pure and Applied Mathematics (CPAM), 65 (8), pp. 1067-1144 (2012). PMID: 24415793 [PubMed] PMCID: PMC3886882.



A. Singer, Z. Zhao, Y. Shkolnisky, R. Hadani, Viewing Angle Classification of Cryo-Electron Microscopy Images using Eigenvectors, SIAM Journal on Imaging Sciences, 4 (2), pp. 543-572 (2011). PMID: 22506089 [PubMed] PMCID: PMC3325115.

A. Singer, Y. Shkolnisky, Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming, SIAM Journal on Imaging Sciences, 4 (2), pp. 543-572 (2011). PMID: 22536457 [PubMed]; PMCID: PMC3334316.

C. Vonesch, L. Wang, Y. Shkolnisky, A. Singer, Fast wavelet-based single-particle reconstruction in cryo-EM, 8th IEEE International Symposium on Biomedical Imaging (ISBI’11), March 30 – April 2, 2011. PMID: 22536462 [PubMed] PMCID: PMC3334313.

C. Ponce, A. Singer, Computing Steerable Principal Components of a Large Set of Images and their Rotations, IEEE Transactions on Image Processing, 20 (11), pp. 3051-3062 (2011). PMID: 21536533 [PubMed - indexed for MEDLINE] PMCID: PMC3719433.

R. Hadani, A. Singer, Representation theoretic patterns in three dimensional Cryo-Electron Microscopy II - The class averaging problem, Foundations of Computational Mathematics (FoCM), 11 (5), pp. 589-616 (2011). PMID: 23239955 [PubMed] PMCID: PMC3519397.

R. Hadani, A. Singer, Representation theoretic patterns in three dimensional Cryo-Electron Microscopy I - The intrinsic reconstitution algorithm, Annals of Mathematics, 174 (2), pp. 1219-1241 (2011). PMID: 23180881 [PubMed] PMCID: PMC3505076.

A. Singer, Angular Synchronization by Eigenvectors and Semidefinite Programming, Applied and Computational Harmonic Analysis, 30 (1), pp. 20-36 (2011). PMID: 21179593 [PubMed] PMCID: PMC3003935.



A. Singer, R. R. Coifman, F. J. Sigworth, D. W. Chester, Y. Shkolnisky, Detecting Consistent Common Lines in Cryo-EM by Voting, Journal of Structural Biology, 169 (3), pp. 312-322 (2010). PMID: 19925867 [PubMed - indexed for MEDLINE] PMCID: PMC2826584.

R. R. Coifman, Y. Shkolnisky, F. J. Sigworth, A. Singer, Reference Free Structure Determination through Eigenvectors of Center of Mass Operators, Applied and Computational Harmonic Analysis, 28 (3), pp. 296-312 (2010). PMID: 20436952 [PubMed] PMCID: PMC2860334.



R. R. Coifman, Y. Shkolnisky, F. J. Sigworth, A. Singer, Graph Laplacian Tomography from Unknown Random Projections, IEEE Transactions on Image Processing, 17 (10):1891-1899 (2008). PMID: 18784036 [PubMed - indexed for MEDLINE]