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Work Email : shai.dekel@ge.com Visiting lecturer at the Tel-Aviv math department PapersAnisotropic function spaces with applications pdf with Pencho Petrushev, in Multiscale, Nonlinear and Adaptive Approximation, Ed. R. DeVore and A. Kunoth, Springer, 2009.
Adaptive compressed image sensing based on wavelet modeling and direct sampling pdf , with Shay Deutsch and Amir Averbuch SAMPTA 2009.
On the equivalence of the modulus of smoothness and the K-functional over convex domains pdf , Approximation Theory, to appear.
Anisotropic meshless frames on R^n pdf with Yongsheng Han and Pencho Petrushev, Fourier Analysis and Applications 15 (2009), 634-662.
Adaptive compressed image sensing based on wavelet-trees pdf , report 2008.
Curvelets: A low-level system for computer vision pdf with Alexander Sherman, report, February 2008.
Two-level splits of anisotropic Besov spaces pdf with Wolfgang Dahmen and Pencho Petrushev, Constructive Approximation , to appear.
Low bit-rate image coding using adaptive geometric piecewise polynomial approximation pdf with Nira Dyn and Roman Kazinnik, IEEE Trans. Image Processing 16 (2007), 2225-2233. Multilevel preconditioning for partition of unity methods - some analytic concepts pdf with Wolfgang Dahmen and Pencho Petrushev, Numerische Mathematik 107 (2007) 503-532. Image coding using geometric wavelets pdf with Dror Alani and Amir Averbuch, IEEE Trans. Image Processing 16 (2007), 69-77. Adaptive multivariate approximation using binary space partitions and geometric wavelets pdf with Dany Leviatan, SIAM Journal on Numerical Analysis 43 (2005), 707-732. See also small erratum Whitney estimates for convex domains with applications to multivariate piecewise polynomial approximation pdf with Dany Leviatan, Foundations of Computational Mathematics 4 (2004), 345-368. The Bramble-Hilbert Lemma for convex domains pdf with Dany Leviatan. SIAM Journal on Mathematical Analysis 35 (2004), 1203-1212. On bivariate smoothness spaces associated with nonlinear approximation pdf with Dany Leviatan and Micha Sharir. Constructive Approximation 20 (2004), 625-646. On the relation of piecewise polynomial and rational approximation in L_p(R^2) pdf with Dany Leviatan. Constructive Approximation 20 (2004), 73-91. On measuring the efficiency of kernel operators in L_p(R^d) pdf with Dany Leviatan. Advances in Computational Mathematics 20 (2004), 53-65. Adaptive multivariate piecewise polynomial approximation, pdf with Dany Leviatan. SPIE Proceedings 5207 (2003), 125-133. Poly-scale refinability and subdivision pdf with Nira Dyn. Applied and Computational Harmonic Analysis 13 (2002), 35-62. Wavelet decompositions of non-refinable shift invariant spaces pdf with Dany Leviatan. Applied and Computational Harmonic Analysis, 12 (2002), 230-258. Nonstationary wavelets, with Dany Leviatan, In Wavelet Analysis, Twenty Years' Developments, Proceedings of the International Conference of Computational Harmonic Analysis, Hong Kong 2001, Ed. Ding-Xuan Zhou.
TeachingMultivariate approximation theory with applications in signal processing, Fall 2009, Tel-Aviv university Students· Shay Deutsch (M.Sc., Adaptive compressed sensing)· Itai Gershtansky (M.Sc., Active geometric wavelets)· Tal Weissblat (Ph.D., Anisotropic function spaces)· Asaf Zarmi (M.Sc., Computer aided diagnosis in orthopedics)PatentsUS 6314452 - Image streaming over the network. With Alexander Ovsiankin. US 7024046 - ‘Scaled’ lossless 2D wavelet transforms and applications. With Nitzan Goldberg US 7376279 - Three-dimensional image streaming. With Nitzan Goldberg and Alexander Sherman. US 7454074 - System for lossless image streaming. With Nitzan Goldberg MeetingsMathematical methods in systems biology, Tel-Aviv, January 2010 Israel Machine Vision, Tel-Aviv, January 2010 Approximation Theory (mini-symposium), San Antonio, US, March 2010 Curves & Surfaces (mini-symposium), Avignon, June 2010 Multivariate Approximation and Interpolation , Edinburgh, September 2010 Mini-Workshop on "Shearlets" Oberwolfach, Germany, October 2010
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“Although it may seem a paradox, all exact science is dominated by the idea of approximation” Bertrand Russell (1872-1970)
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