Review Papers

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


Particle Picking

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

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.

CTF Estimation

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


3-D Heterogeneity Analysis:

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

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).

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, 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.

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).

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.

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 ProblemSIAM Journal on Imaging Sciences, 8 (1), pp. 126-185 (2015). PMID: 25699132 [PubMed] PMCID: PMC4331039


3-D Ab-initio Modeling using Kam's Theory: 

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. 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.

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.

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

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

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


3-D Ab-initio Modeling without particle picking: 

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.-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

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).


3-D Ab-Initio Modeling using Common lines:

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

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

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

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

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.

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, 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.

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.


2-D Class Averaging:

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

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

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.

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

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, 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.


Steerable PCA:

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).

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.

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

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.

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.


Image Restoration: 

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

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 ImagesJournal of Structural Biology, 195 (1), pp. 72-81 (2016). PMID:27129418 [PubMed - in process]


3-D Tomographic Inversion:

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.


2-D Tomography:

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

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]


Wilson Statistics

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

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


Multi-Reference Alignment

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. 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

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. 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).​

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.

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.


Multi-Target Detection

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).

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.-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


Representation Theory:

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.


Angular Synchronization:

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.

Validation and Fourier Shell Correlation:
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