Nir Sharon

Senior Lecturer in Applied Mathematics School of Mathematical SciencesTel Aviv University

Office: 121 Schreiber building
Office phone: 03-640-6375
Email: nsharon at tauex.tau.ac.il

Main research interests:
Approximation on manifolds, Estimation problems over groups, Mathematics of electron microscopy, Geometric modelling, Numerical algorithms, Applied harmonic analysis.

Publications

Preprint

1. N. Sharon, V. Peiris, N. Sukhorukova, J. Ugon. Flexible rational approximation and its application for matrix functions. 2022. URL https://arxiv.org/abs/2108.09357. Submitted.

2. W. Mattar, N. Sharon. Pseudo-reversing and its application for multiscaling of manifold-valued data. 2023. URL https://arxiv.org/abs/2305.06261. Submitted.

3. I. Hadi, T. Bendory, N. Sharon. SE(3) Synchronization by Eigenvectors of Dual Quaternion Matrices. 2023. URL https://arxiv.org/abs/2307.07640. Submitted.

4. H. Ben Zion Vardi, N. Dyn, N. Sharon. Hermite subdivision schemes for manifold-valued Hermite data. 2023. Submitted.

Peer-review journals

1. Y. Khoo, S. Paul, N. Sharon. Deep Neural Network Prior for Orbit Recovery from Method of Moments. Journal of Computational and Applied Mathematics 115782, 2024

2. N. Sharon, R. Sherbu Cohen, H. Wendland . On multiscale quasi-interpolation of scattered scalar- and manifold-valued functions. SIAM Journal on Scientific Computing. 45(5), A2458-A2482, 2023

3. H. Ben Zion Vardi, N. Dyn, N. Sharon. Geometric Hermit Interpolation in $R^n$ by refinements. Advances in Computational Mathematics 49(38). 2023

4. T. Bendory, I. Hadi, N. Sharon. Compactification of the Rigid Motions Group in Image Processing. SIAM Journal on Imaging Sciences 15(3), 1041-1078. 2022

5. A. Abas, T. Bendory, N. Sharon. The generalized method of moments for multireference alignment. IEEE Transactions on Signal Processing, 70, 1377-1388. 2022

6. T. Bendory, D. Edidin, W. Leeb, N. Sharon. Dihedral multireference alignment. IEEE Transactions on Information Theory 68(5), 3489-3499. 2022

7. W. Mattar and N. Sharon. Pyramid transform of manifold data via subdivision operators. IMA Journal on Numerical Analysis. https://doi.org/10.1093/imanum/drab095. 2021.

8. A. Heimowitz, N. Sharon, and A. Singer. Centering noisy images with application to cryo-EM. SIAM Journal on Imaging Sciences, 14(2), 689-716, 2021

9. T. Bendory, A. Jaffe, W. Leeb, N. Sharon, A. Singer. Super-resolution multireference alignment. Information and Inference: a Journal of the IMA, iaab003, https://doi.org/10.1093/imaiai/iaab003, 2021

10. V. Peiris, N. Sharon, N. Sukhorukova J. Ugon. Rational approximation and its application to improving deep learning classifiers. Applied Mathematics and Computation, 389:125560, 2021

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

12. R. Mitz, N. Sharon, and Y. Shkolnisky. Out-of-sample extension based on rank-one updating with partial spectrum. SIAM Journal on Matrix Analysis and Applications, 40(3): 973-997, 2019

13. E. Abbe, T. Bendory, W. Leeb, J. M. Pereira, N. Sharon, and A. Singer. Multireference alignment is easier with an aperiodic translation distribution.IEEE Transactions on Information Theory, 65(6), 3565-3584, 2018

14. N. Sharon and Y. Shkolnisky. Evaluating non-analytic functions of matrices. Journal of Mathematical Analysis and Applications, 462(1):613–636, 2018

15. O. Ozyesil, N. Sharon, and A. Singer. Synchronization over Cartan motion groups via contraction. SIAM Journal on Applied Algebra and Geometry (SIAGA), 2(2): 207-241, 2018

16. N. Dyn and N. Sharon. Manifold-valued subdivision schemes based on geodesic inductive averaging. Journal of Computational and Applied Mathematics, 311:54–67, 2017

17. N. Dyn and N. Sharon. A global approach to the refinement of manifold data. Mathematics of Computation, 86(303):375–395, 2017

18. V. May, Y. Keller, N. Sharon, and Y. Shkolnisky. An algorithm for improving non-local means operators via low-rank approximation. IEEE Transactions on Image Processing, 25(3):1340–1353, 2016

19. N. Dyn, A. Heard, K. Hormann, and N. Sharon. Univariate subdivision schemes for noisy data with geometric applications. Computer Aided Geometric Design, 37:85–104, 2015

20. N. Sharon and Y. Shkolnisky. A class of laplacian multiwavelets bases for high-dimensional data. Applied and Computational Harmonic Analysis, 38(3):420–451, 2015

21. N. Sharon and U. Itai. Approximation schemes for functions of positive-definite matrix values. IMA Journal of Numerical Analysis, 33(4):1436–1468, 2013

22. U. Itai and N. Sharon. Subdivision schemes for positive definite matrices. Foundations of Computational Mathematics, 13(3):347–369, 2013

23. N. Sharon and N. Dyn. Bivariate interpolation based on univariate subdivision schemes. Journal of Approximation Theory, 164(5):709–730, 2012

Unpublished

1. N. Sharon and J. Zandberg. Strategic alliances under risk adjusted payoffs. SSRN, 2017. URL https://ssrn.com/abstract=3020968.

2 N. Dyn, U. Itai, and N. Sharon. Approximation operators for matrix-valued functions based on matrix decomposition. 2014. URL https://arxiv.org/abs/1611.03893.

Funding

U.S.-Israel Binational Science Foundation (BSF)

The Research and Development Authority - BSF and
NSF-BSF Visit to BGU

NSF-BSF joint program

TAU-Swinburne Research Collaboration

German Research Foundation (DFG)

Teaching 22-23

Spring 24 graduate level:

CLASSICAL APPROXIMATION METHODS AND EXTENSION TO MANIFOLDS, see here.

Spring 24: Advanced Seminar in Applied Mathematics, see description

Winter 24: Numerical Analysis (undergraduate course), see here.

Previous teaching (2019-2022): Advanced graduate level course: Estimation Problems over Groups, see here

current Research group

Graduate Students

Ido Hadi
Wael Mattar
Asaf Abas

Master Students

Lev Kapnulin
Orel Levy
Maayan Yesharim
Hadar Landau
Gil Drozatz
Guy Hay
Noam Cayron