Multi-reference Alignment

E. Abbe, T. Bendory, W. Leeb, J. Pereira, N. Sharon, A. Singer, Multireference Alignment is Easier with an Aperiodic Translation Distribution, arXiv preprint.

N. Boumal, T. Bendory, R. R. Lederman, A. Singer, Heterogeneous multireference alignment: a single pass approach, arXiv preprint.

A. Perry, J. Weed, A. S. Bandeira, P. Rigollet, A. Singer, The sample complexity of multi-reference alignment, arXiv preprint.

T. Bendory, N. Boumal, C. Ma, Z. Zhao, A. Singer, Bispectrum Inversion with Application to Multireference Alignment, IEEE Transactions on Signal Processing, accepted.

E. Abbe, J. Pereira, A. Singer, Sample Complexity of the Boolean Multireference Alignment ProblemIEEE International Symposium on Information Theory (ISIT), pp. 1316-1320, 2017.

 

Heterogeneity:

J. Andén, A. Singer, Structural Variability from Noisy Tomographic Projections, arXiv preprint. 

R. R. Lederman, A. Singer, Continuously heterogeneous hyper-objects in cryo-EM and 3-D movies of many temporal dimensions, arXiv preprint.

R. R. Lederman, A. Singer, A Representation Theory Perspective on Simultaneous Alignment and Classification, arXiv preprint.

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

 

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

E. Levin, T. Bendory, N. Boumal, J. Kileel, A. Singer, 3D ab initio modeling in cryo-EM by autocorrelation analysis, arXiv preprint.

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 Applications524, pp. 159-181 (2017).  NIHMSID: NIHMS867571. 

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

 

3D Ab-Initio Modeling using Common lines:

A. S. Bandeira, Y. Chen, A. Singer, Non-Unique Games over Compact Groups and Orientation Estimation in Cryo-EM, arXiv preprint.

I. Greenberg, Y. Shkolnisky, Common Lines Modeling for Reference Free Ab-Initio Reconstruction in Cryo-EMJournal of Structural Biology, in press, 2017.

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.

 

2D Class Averaging:

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:

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: 

J. Andén, A. Singer, Factor Analysis for Spectral EstimationSampling Theory and Applications (SampTA), 12th International Conference, pp. 169-173, 2017.

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]

 

3D 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.

 

2D 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]

 

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.