Nir Sharon

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

3. G. Hay and N.Sharon. Function Extrapolation with Neural Networks and Its Application for Manifolds. https://arxiv.org/abs/2405.10563. Submitted.

4. L. Lahat. C. Sharoni, G. Van Dam, N. Sharon. The Relationship Between Perceptions of Social Service Quality and Well-being. Submitted.

5. A. Banerjee, H. Lee, N. Sharon, C. Moosmüller. Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging. https://arxiv.org/abs/2405.19679. Submitted.

6. W. Mattar, I. Levy, N. Sharon, S. Dekel. Wavelets Are All You Need for Autoregressive Image Generation. http://arxiv.org/abs/2406.19997. Submitted.

Peer-review journals

1. I. Hadi, T. Bendory, N. Sharon. SE(3) Synchronization by Eigenvectors of Dual Quaternion Matrices. Information and Inference: A Journal of the IMA. To appear, 2024.
2. H. Ben Zion Vardi, N. Dyn, N. Sharon. Hermite subdivision schemes for manifold-valued Hermite data. Computer Aided Geometric Design. 102342. 2024.

3. 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.

4. 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

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

6. 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

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

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

9. 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.

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

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

17. 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

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

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

20. 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

21. 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

22. 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

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

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

25. 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: 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
Vladimir Yevsukov
Erel Panijel