## Publications

Sparse Besov space analysis of deep learning representation layers in high dimensions, pdf, with Ido Ben-Shaul and Oren Elisha, Pure and Applied Functional Analysis, to appear.

Reverse engineering self-supervised learning, with Ido Ben-Shaul, Ravid Shwartz-Zvi, Tomer Galanti and Yann LeCun, pdf, NeurIPS 2023.

Numerical methods for PDEs over manifolds using spectral physics informed neural networks, pdf (revised) with Yuval Zelig, submitted.

Exploring the approximation capabilities of multiplicative neural networks for smooth functions, pdf, with Ido Ben-Shaul and Tomer Galanti, TMLR 2023.

PR-DAD: Phase retrieval using deep auto-decoders, with Leon Gugel, pdf, ICFSP 2022.

Pointwise variable anisotropic function spaces on R^n, pdf (preprint format), De Gruyter Studies in Mathematics Vol. 85 (2022)

Nearest class center simplification through intermediate layers, with Ido Ben-Shaul, PMLR 196 (2022).

A physically-informed deep-learning model using time-reversal for locating a source from sparse and highly noisy sensors data, with Dan Givoli, Adar Kahana and Eli Turkel, pdf, Journal of computational physics 470 (2022).

Sparsity-Probe: analysis tool for deep learning models, with Ido Ben-Shaul, pdf, IMVC 2021. Talk @ Tel-Aviv seminar

video - visualization of the unfolding process (UMAP of functional geometric VGG-13 inner layer representations of CIFAR10 dataset)

Beyond the Courant-Friedrichs-Lewy condition: Numerical methods for the wave problem using deep learning, with Adar Kahana, Oded Ovadia and Eli Turkel, pdf, Journal of computational physics 442 (2021),

Obstacle segmentation based on the wave equation and deep learning, with Dan Givoli, Adar Kahana and Eli Turkel, pdf, Journal of computational physics 413 (2020).

Function space analysis of deep learning representation layers, with Oren Elisha, arXiv.

Wavelet decomposition of Gradient Boosting, with Oren Elisha and Ohad Morgan, arXiv, GitLab code.

Stable recovery of stream of pulses with application to ultrasound Imaging, pdf, with Dan Adam, Avinoam Bar-Zion, Tamir Bendory and Arie Feuer, IEEE Transactions of signal processing, 64 (2016), 3750-3759.

Wavelet decompositions of Random Forests - smoothness analysis, sparse approximation and applications pdf , with Oren Elisha, Journal of machine learning research 17 (2016).

A Mathematical Model for Adaptive Computed Tomography Sensing, pdf, with Oren Barkan, Jonathan Weill and Amir Averbuch, , IEEE Transactions on computational imaging 3 (2017), 551-565.

Robust recovery of streams of pulses using convex optimization, pdf, with Tamir Bendory and Arie Feuer, Journal of mathematical analysis and applications 442 (2016), 511-536.

Hardy spaces associated with non-negative self-adjoint operators (revised), pdf , with Gerard Kerkyacharian, George Kyriazis and Pencho Petrushev, Studia Mathematica 239 (2017), 17-54.

A new proof of the atomic decomposition of Hardy spaces, pdf with Gerard Kerkyacharian, George Kyriazis and Pencho Petrushev, Proceedings of constructive theory of functions 2016, 59-73.

Super-resolution on the sphere using convex optimization, pdf, with Tamir Bendory and Arie Feuer, IEEE Transactions on signal processing 63 (2015), 2253-2262.

Computer aided diagnostics in digital pathology: Automated evaluation of early phase pancreatic cancer in mice, pdf, with Moran Amit, Yoav Binenbaum, Ziv Gil, Leon Gugel and Leeor Langer, Journal of computer assisted radiology and surgery 10 (2015), 1043-1054.

Exact recovery of Dirac ensembles from the projection onto spaces of spherical harmonics, pdf, with Tamir Bendory and Arie Feuer, Constructive Approximation 42 (2015), 183-207.

Wavelet decompositions of random forests, pdf , with Iryna Nemirovsky, technical report 2014.

Exact recovery of non-uniform splines from the projection onto spaces of algebraic polynomials, pdf, with Tamir Bendory and Arie Feuer, Approximation Theory 182 (2014), 7-17.

Compactly supported frames for spaces of distributions associated with non-negative self-adjoint operators, pdf, with Gerard Kerkyacharian, George Kyriazis and Pencho Petrushev , Studia Mathematica 225 (2014), 115-163.

A mathematical model for extremely low dose adaptive computed tomography acquisition, pdf, with Amir Averbuch, Oren Barkan and Yaniv Tenzer, Lecture notes in computer science 8177 (2014), 13-33.

On dual spaces of anisotropic Hardy spaces, pdf with Tal Weissblat, Mathematische Nachrichten 17-18 (2012), 2078-2092.

On the analysis of anisotropic smoothness, pdf , Approximation Theory 164 (2012), 1143-1164.

Adaptive compressed image sensing using dictionaries, pdf , with Shay Deutsch and Amir Averbuch, SIAM Journal of imaging sciences 5 (2012), 57-89.

Hardy spaces on R^n with pointwise variable anisotropy, pdf with Pencho Petrushev and Tal Weissblat, Fourier Analysis and Applications 17 (2011), 1066-1107.

Active Geometric Wavelets, pdf with Itai Gershtansky, in proceedings Approximation Theory XIII: San Antonio 2010(2012), 95-109.

On the equivalence of the modulus of smoothness and the K-functional over convex domains pdf , Approximation Theory 162 (2010), 349-362.

Two-level splits of anisotropic Besov spaces pdf with Wolfgang Dahmen and Pencho Petrushev, Constructive Approximation 31 (2010), 149-194.

Adaptive compressed image sensing based on wavelet modeling and direct sampling pdf , with Shay Deutsch and Amir Averbuch, proceedings SAMPTA 2009.

Anisotropic function spaces with applications pdf with Pencho Petrushev, in Multiscale, Nonlinear and Adaptive Approximation, Ed. R. DeVore and A. Kunoth, Springer, 2009.

Curvelets: A low-level system for computer vision pdf with Alexander Sherman, report, February 2008.

Anisotropic meshless frames on R^n pdf with Yongsheng Han and Pencho Petrushev, Fourier Analysis and Applications 15 (2009), 634-662.

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.

On shift invariant spaces, wavelets and subdivision in the absence of two-scale refinability, PhD thesis, pdf, 2000.

Generators of Sn and An, M.Sc. thesis, pdf, Tel-Aviv University, 1994.