RESEARCH WORKS OF ALBERT COHEN
I. BOOKS
[L1] A. Cohen, Ondelettes et traitement numerique du signal,
RMA25, Masson, Paris, 1992.
[L2] A. Cohen and R. Ryan, Wavelets and Multiscale Signal Processing,
Chapman and Hall, London, 1995.
[L3] A. Cohen, Numerical analysis of wavelet methods,
Studies in mathematics and its applications, Elsevier, Amsterdam, 2003
II. INVITED SURVEYS
[S1] A. Cohen and R. DeVore, Approximation of high-dimensional PDEs,
Acta Numerica, vol. 24, 1-159, 2015.
[S2] A. Cohen, A journey through the Mathematics of Yves Meyer,
The Abel Prize 2013-2017 (Eds. H. Holden and R. Piene), 1-54, Springer, 2018.
II. JOURNAL PAPERS
[A1] A. Cohen, Ondelettes, analyses multiresolutions et filtres miroirs en quadrature,
Annales de l'IHP, Analyse non-lineaire, vol.7, 439-459, 1990.
[A2] A. Cohen, Construction de bases d'ondelettes alpha-Holderiennes,
Revista Matematica Iberoamericana, vol.6, 91-108, 1991.
[A3] A. Cohen, J. Froment and J. Istas, Analyse multiresolution de signaux aleatoires,
CRAS t.312, Serie I, p.567-570, 1991.
[A4] A. Cohen and J.P. Conze, RŽgularitŽ des bases d'ondelettes et mesures ergodiques,
Revista Matematica Iberoamericana, vol. 8, 351-365, 1992.
[A5] A. Cohen, I. Daubechies and J. C. Feauveau, Biorthogonal bases of
compactly supported wavelets, Comm. in Pure and Appl. Math., vol. 45, 485-560, 1992.
[A6] A. Cohen and I. Daubechies, A stability criterion for biorthogonal
wavelets and their related subband coding schemes,
Duke Journal of Mathematics, vol. 68, 313-335, 1992.
[A7] A. Cohen and I. Daubechies, Orthonormal bases of compactly supported wavelets,
variations on a theme III: Better frequency localisation,
SIAM Journal of Math. Anal., vol.24-2, 520-527, 1993.
[A8] A. Cohen and I. Daubechies, Non-separable bidimensional wavelet bases,
Revista Matematica Iberoamericana, vol.9-1, 51-137, 1993.
[A9] A. Cohen and J.M. Schlenker, Compactly supported wavelets
with hexagonal symmetry, Constructive Approximation, vol.9, 209-236, 1993.
[A10] A. Cohen and Q. Sun, An arithmetic characterization of the conjugate
quadrature filters associated to orthonormal wavelet bases,
SIAM Journal of Math. Anal., vol.24-5, 1355-1360, 1993.
[A11] A. Cohen, I. Daubechies and P.Vial, Wavelets and fast wavelet transforms
on an interval, Applied and Computational Harmonic Analysis, vol.1-1, 1993.
[A12] A. Cohen and I. Daubechies, On the instability of biorthogonal wavelet packets,
SIAM Journ. of Math. Anal, vol.24-5, 1340-1354, 1993.
[A13] A. Cohen, I. Daubechies, P. Vial and B. Jawerth, Multiresolution analysis,
wavelets and fast algorithms on an interval, CRAS t.316, Serie I, p.417-421, 1993.
[A14] A. Cohen, I. Daubechies and A. Ron, How smooth is the smoothest function
in a refinable space, ACHA, vol.3, 87-89, 1996.
[A15] A. Cohen and I. Daubechies, A new technique to estimate the regularity
of refinable functions, Rev. Mat. Iberoam., vol.12, 2, 527-591, 1996.
[A16] A. Cohen and N. Dyn, Nonstationary subdivision schemes and
multiresolution analysis, SIAM J. Math. Anal. 27, 1745-1769, 1996.
[A17] A. Cohen and A. Ezzine, Quadratures singulieres et fonctions d'echelle,
CRAS, t.323, Serie I, 829-834, 1996.
[A18] A. Cohen and J.P. D'Ales, Non-linear approximation of random functions,
SIAM J. Appl. Math. 57, 518-540, 1997.
[A19] A. Cohen, I. Daubechies and G. Plonka, On the regularity of
refinable vectors, J. Fourier Anal. and Appl. 3, 295-324, 1997.
[A20] A. Cohen and J. Kovacevic, Wavelets: the mathemactical background,
IEEE Trans. Signal Processing, special issue on wavelets 1998.
[A21] A. Cohen, K. Grochenig and L. Villemoes, On the regularity of multivariate
refinable functions, Constr. Approx.15, 241-255, 1999.
[A22] A. Cohen, F. Moreau and P. Siohan, Biorthogonal filter banks and energy
conservation, IEEE Trans. Image processing 8, 168-178, 1999.
[A23] A. Cohen, R. DeVore, P. Petrushev and H. Xu, Non linear approximation and the
space BV(R2), Amer. J. Math. 121, 587-628, 1999.
[A24] A. Cohen and R. Masson, Wavelet methods for second order elliptic
problems - preconditioning and adaptivity, SIAM J. Sci. Comp. 21, 1006-1026, 1999.
[A25] A. Cohen and R. Danchin, Multiscale approximation of vortex patches,
SIAM J. Appl. Math. 60, 477-501, 2000.
[A26] A. Cohen, N. Dyn, S.-M. Kaber and M. Postel, Multiresolution schemes on
triangles for scalar conservation laws, J. Comp. Phys. 161, 264-286, 2000.
[A27] A. Cohen, R. DeVore and R. Hochmuth, Restricted nonlinear approximation,
Constructive Approximation 16, 85-113, 2000.
[A28] A. Cohen and R. Masson, Wavelet adaptive method for second order
elliptic problems - boundary conditions and domain decomposition,
Numer. Math. 86, 193-238, 2000.
[A29] A. Cohen, R. DeVore and W. Dahmen, Multiscale methods on bounded domains,
Trans. AMS 352, 3651-3685, 2000.
[A30] A. Cohen, R. DeVore and W. Dahmen, Adaptive wavelet methods fo elliptic
operator equations - convergence rates, Math. Comp. 70, 27-75, 2000.
[A31] A. Cohen et B. Perthame, Optimal approximation orders for transport
equations by pseudo-particle methods, SIAM J. Math. Anal. 32, 616-636, 2001.
[A32] A. Cohen, R. DeVore, G. Kerkyacharian and D. Picard, Maximal spaces
with given rate of convergence for thresholding algorithms,
Applied an Computational Harmonic Analysis 11, 167-191, 2001
[A33] A. Cohen, W. Dahmen, I. Daubechies and R. DeVore, Tree approximation
and optimal encoding, Applied and Computational Harmonic Analysis 11, 192-226, 2001.
[A34] A. Barinka, T.Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen and K.Urban,
Adaptive Wavelet Schemes for Elliptic Problems - Implementation and Numerical Experiments,
SIAM J. Sci. Comput.23, 910-939, 2001.
[A35] S. Amat, F. Arandiga, A. Cohen, R. Donat, G. Garcia and M. Von Oehsen,
Data compression with ENO schemes - a case study,
Appl. Comput. Harmon.Anal.11, 273-288, 2002.
[A36] A. Cohen, S. Mueller, M. Postel and S.M. Ould-Kaber, Fully adaptive
multiresolution schemes for conservation laws, Math. Comp. 72, 183-225, 2002.
[A37] A. Cohen, I. Daubechies, M. Orchard and O. Gulieriz, On the importance
of combining wavelet-based non-linear approximation with coding strategies,
IEEE Trans. Inf. Theory 48-7, 2002.
[A38] A. Cohen, W. Dahmen and R. DeVore, Adaptive wavelet methods - beyond
the elliptic case, Found. of Comp. Math. 2, 203-245, 2002.
[A39] S. Amat, F. Arandiga, A. Cohen and R. Donat, Tensor product multiresolution
analysis with error control for compact image representations,
Signal Processing 82, 587-608, 2002.
[A40] A. Cohen, N. Dyn and B. Matei, Quasilinear subdivision schemes with
applications to ENO interpolation,
Applied and Computational Harmonic Analysis 15, 89-116, 2003
[A41] A. Cohen, W. Dahmen, I. Daubechies and R. DeVore, Harmonic analysis of
the space BV, Revista Mathematica Iberoamericana 19, 235-263, 2003.
[A42] A. Cohen, W. Dahmen and R. DeVore, Sparse multiscale evaluation of
nonlinear composition of functions, SIAM J. Math. Anal. 35, 279-303, 2003.
[A43] A. Cohen, W. Dahmen and R. DeVore, Adaptive wavelet scheme for nonlinear
variational problems with convergence rates, SIAM J. Numer. Anal. 41, 1785-1823, 2003.
[A44] A. Cohen, W. Dahmen and R. DeVore, Adaptive wavelet techniques in numerical
simulation, Encyclopedia of Computational Mathematics, Vol. 1, 157-197, 2004.
[A45] A. Cohen, M. Hoffmann and M. Reiss, Adaptive wavelet-galerkin
methods for inverse problems, SIAM J. Num. Anal. 42, 1479-1501, 2004.
[A46] F.Arandiga, A. Cohen, R. Donat and N. Dyn, Interpolation and approximation
of piecewise smooth functions, SIAM J. Numer. Anal. 43-1, 41-57, 2005.
[A47] M. Campos Pinto, A. Cohen, W. Dahmen and R. DeVore, On the stability
of conservation laws in the Hausdorff metric, JDHE 2, 25-38, 2005.
[A48] M. Campos Pinto, A. Cohen and P. Petrushev, High order geometric smoothness
of conservation laws, JDHE 2, 39-61, 2005.
[A49] P. Binev, A. Cohen, W. Dahmen, R. DeVore and V. Temlyakov, Universal
algorithms in learning theory - Part I : piecewise constant functions, JMLR 6,
1297-1321, 2005.
[A50] P. Binev, A. Cohen, W. Dahmen and R. DeVore, Universal algorithms in
learning theory - Part II : piecewise polynomial functions, Constructive
Approximation 26, special issue on learning theory, 127-152, 2007.
[A51] A. Cohen, Approximation by greedy algorithms, SIAM News, 2007.
[A52] A. Barron, A. Cohen, W. Dahmen and R. DeVore, Approximation and
learning by greedy algorithms, Annals of Statistics 36-1, 64-94, 2008.
[A53] F. Arandiga, A. Cohen, R. Donat, N. Dyn and B. Matei, Approximation
of piecewise smooth images by edge-adapted techniques, ACHA 24, 225-250, 2008.
[A54] R. Baraniuk, A. Cohen and R.Wagner, Approximation and compression
of scattered data by meshless multiscale decompositions, ACHA 25, 133-147, 2008.
[A55] A. Cohen, R. DeVore and W. Dahmen, Compressed sensing and
best k-term approximation, Journal of the AMS 22, 211-231, 2009.
[A56] F. Arandiga, A. Cohen, R. Donat and B.Matei, An edge detector
insensitive to illumination changes in the image, to appear in IMAVIS, 2009.
[A57] A. Cohen and J.-M. Mirebeau, Anisotropic smoothness classes : from finite
element approximation to image models, J. Math Imaging and Vision 38, 52-69, 2010.
[A58] A. Cohen, R. DeVore and C. Schwab, Convergence Rates of Best N-term
Galerkin Approximations for a Class of Elliptic sPDEÕs, J. FoCM 10, 615-646, 2010.
[A59] H. Bahouri and A. Cohen, Refined Sobolev embedding in
Lorentz spaces, JFAA 17, 662-673, 2011.
[A60] A. Cohen, R. DeVore and C. Schwab, Analytic regularity and
polynomial approximation of parametric and stochastic PDEÕs,
Analysis and Applications 9, 11-47, 2011
[A61] H. Bahouri, A. Cohen and G. Koch, A general wavelet-based profile
decomposition in the critical embedding of function spaces,
Confluentes Matematicae 3, 387-411, 2011.
[A62] P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk,
Convergence rates for greedy algorithms in the reduced basis method,
SIAM J. Math. Anal 43, 1457-1472, 2011.
[A63] A. Cohen, Sur la route des ondelettes,
Gazette des mathematiciens 130, SMF, 19-35, 2011.
[A64] A. Cohen, N. Dyn, F. Hecht and J.-M. Mirebeau, Adaptive multiresolution analysis
based on anisotropic triangulations, Math. of Comp. 81, 789-810, 2012.
[A65] A. Cohen and J.-M. Mirebeau, Greedy bisection generates optimally
adapted triangulations, Math. of Comp. 81, 811-837, 2012.
[A66] A. Cohen, R. DeVore, G.Kerkyacharian and D.Picard, Capturing ridge functions
in high dimension from point queries, Constructive Approximation 35, 225-243, 2012.
[A67] A. Cohen, R. DeVore and R.Nochetto, Convergence rates for AFEM with H-1 data,
JfoCM 12, 671-718, 2012.
[A68] A. Cohen, W. Dahmen and G. Welper, Adaptivity and variational stabilization
for convection diffusion equations, M2AN 46, 1247-1273, 2012.
[A69] A. Chkifa, A. Cohen, R. DeVore and C. Schwab, Sparse adaptive Taylor
approximation algorithms for parametric and stochastic PDEÕs, M2AN 47-1, 253-280, 2013.
[A70] A. Cohen, M. Davenport and D. Leviatan, On the stability and accuracy
of least-squares approximations, JFoCM 5, 819-834, 2013.
[A72] F. Arandiga, A. Cohen and D. Yanez, Learning-based multiresolution transforms
with applications to image compression, Signal Processing 93, 2474-2484, 2013.
[A73] A. Cohen, R. DeVore, G. Petrova and P. Wojtaszczyk, Finding the minimum of
a function, Methods and Applications of Analysis 20-4, 393-410, 2013.
[A74] A. Chkifa, A. Cohen and C. Schwab, High-dimensional adaptive sparse
polynomial interpolation and application to parametric PDEs, JfoCM 14, 601-633, 2014.
[A75] G. Chardon, A. Cohen and L. Daudet, Approximation of solutions to the
Helhmoltz equation from scattered data, Sampling Theory in Signal Analysis
and Image Processing 13, 2014.
[A76] P. Binev, A. Cohen, W. Dahmen and R. DeVore, Classification algorithms
using adaptive partitioning, Annals of Statistics 42-6, 2141-2163, 2014.
[A77] A. Chkifa, A. Cohen and C. Schwab, Breaking the curse of dimensionality
in sparse polynomial approximation of parametric PDEs, Journal de Mathematiques
Pures et Appliquees 103, 400-428, 2015.
[A78] A. Chkifa, A. Cohen, G. Migliorati, F. Nobile and R. Tempone, Discrete
least squares polynomial approximation with random evaluations - Application to
parametric and stochastic elliptic PDEs, M2AN 49, 815-837, 2015.
[A79] A. Cohen and R. DeVore, Kolmogorov n-widths under holomorphic mappings,
IMA Journal of numerical analysis 36-1, 1-12, 2016.
[A80] M. Bachmayr and A. Cohen, Kolmogorov widths and low-rank approximations
of parametric elliptic PDEs, Mathematics of Computation 86, 701-724, 2017.
[A81] A. Cohen, W. Dahmen and R. DeVore, Orthogonal matching pursuit under
the restricted isometry property, Constructive Approximation 45, 113-127, 2017.
[A82] M. Bachmayr, A. Cohen and G. Migliorati, Sparse polynomial approximation
of parametric elliptic PDEs Part I: affine coefficients, M2AN 51, 321-339, 2017.
[A83] M. Bachmayr, A. Cohen, R. DeVore and G. Migliorati, Sparse polynomial approximation
of parametric elliptic PDEs Part II: lognormal coefficients, M2AN 51, 341-363, 2017.
[A84] P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk,
Data assimilation in reduced modeling, SIAM/ASA J. Uncertain. Quantif. 5, 1-29, 2017.
[A85] A. Cohen, G. Migliorati and F. Nobile, Discrete least-squares approximations
over optimized downward closed polynomial spaces in arbitrary dimensions,
Constructive approximation 45, 497-519,2017.
[A86] M. Bachmayr, A. Cohen, C. Schwab and D. Zhung,
Fully discrete approximation of parametric and stochastic elliptic PDEs,
SIAM J. Num. Anal. 55, 2151-2186, 2017.
[A87] A. Bonito, A. Cohen, R. DeVore, G. Petrova and G. Welper, Diffusion Coefficients Estimation for Elliptic Partial Differential Equations, SIAM J. Math. Anal 49. 1570-1592, 2017.
[A88] A. Cohen and G. Migliorati, Optimal weighted least-squares methods, SMAI J. Comp. Math. 3, 181-203, 2017.
[A89] M. Bachmayr, A. Cohen and G. Migliorati, Representations of Gaussian
random fields and approximation of elliptic PDEs with lognormal coefficients,
J. Fourier Anal. Appl. 24, 621-649, 2018.
[A90] A. Cohen, C. Schwab and J. Zech,
Shape Holomorphy of the stationary Navier-Stokes Equations, SIAM J. Math. Anal. 50, 1720-1752, 2018.
[A91] M. Bachmayr, A. Cohen and W. Dahmen,
Parametric PDEs: Sparse or low-rank approximations?, to appear in IMA J. Num. Anal., 2018.
[A92] P. Binev, A. Cohen, O. Mula and J. Nichols,
Greedy algorithms for optimal measurements selection in state estimation using reduced models,
to appear in SIAM/ASA J. Uncertain. Quantif. 2018.
III. PROCEEDINGS AND BOOK CHAPTERS
[C1] A. Cohen, Wavelets and digital signal processing,
in Wavelets, ed. Ruskai and al., Jones and Bartlett, 1992.
[C2] A. Cohen, Biorthogonal wavelets, in Wavelets and Applications, ed
C.K. Chui, Academic Press, 1992.
[C3] A. Cohen and J.Froment, Image compression and multiscale approximation,
in Wavelets and applications (Marseille, Juin 89), ed. Y.Meyer, Masson, 1992.
[C4] A. Cohen, Wavelets, approximation theory and subdivision schemes,
Approximation Theory VII (Austin, 1992), ed. E.W. Cheney and al., Academic Press, 1993.
[C5] A. Cohen, Biorthogonal wavelets and dual filters,
Advances in image communication, vol.5, M.Barlaud eds., Elsevier, 1-26, 1994.
[C6] A. Cohen and J.P. D'Ales, Nonlinear approximation of stochastic processes,
Lecture Notes in Statistics, vol. 103, A.Antoniadis and G.Oppenheim eds.,
Springer Verlag, 109-124, 1995.
[C7] A. Cohen, Nonlinear wavelet approximation and image compression,
Approximation Theory VIII, vol.2, C.K. Chui and L.L.Schumaker eds.,
World Scientific, 17-38, 1995.
[C8] A. Cohen, N. Dyn and D.Levin, Stability and interdependence of matrix
subdivision schemes, in proceedings of Advanced Topics in Multivariate Approximation,
(Montecatini 95) Fontanella, Jetter and Laurent eds., World Scientific, 1996.
[C9] A. Cohen and E. Sere, Time-frequency localization with non-stationary
wavelet packets, in Subband and wavelet transforms - theory and design,
M.T.Smith and A.Akansu eds., Kluwer, 1996.
[C10] A. Cohen and N. Dyn, Non-stationary wavelets and wavelet-packets,
Proc. Neamann Workshop (Haifa May 94), J.Zeevi ed., Acad. Press, 1997.
[C11] A. Cohen, Wavelets in image processing, Proc. conf. Image
techno-fair (Chiba, Japan 96), 1997.
[C12] A. Cohen, Y.Meyer and F.Oru, Improved Sobolev inequalities,
actes seminaires X-EDP, 1998
[C13] A. Cohen, Ondelettes, espaces d'interpolation et applications,
Proc. X-EDP 99-00, Palaiseau, 2000.
[C14] A. Cohen, Wavelet methods in Numerical Analysis, Handbook of Numerical
Analysis, vol. VII, P.G. Ciarlet and J.L.Lions eds., Elsevier, Amsterdam, 2000.
[C15] A. Cohen, Applied and computational aspects of nonlinear
wavelet approximation, Multivariate approximation and applications 188-212,
Cambridge Univ. Press, Cambridge, 2001.
[C16] A. Cohen and B.Matei, Compact representations of images by edge adapted
multiscale transforms, IEEE ICIP conference, Tessaloniki, 2001.
[C17] A. Cohen, S.M.Kaber and M.Postel, Multiresolution analysis on triangles
application to gaz dynamics, International series of numerical mathematics,
vol. 140, Birkhauser, 2001.
[C18] A. Cohen, Ondelettes et Applications, Techniques de l'Ingenieur, 2002.
[C19] A. Cohen and B.Matei, Nonlinear subdivisions schemes: applications
to image processing, Tutorial on multiresolution in geometric modelling,
A.Iske, E.Quack and M.Floater eds., Srpinger, 2002.
[C20] A. Cohen, Adaptive multiscale methods for evolution equations,
proceedings of ENUMATH conference (Ischia 2001), 2002
[C21] A. Cohen, Adaptive methods for PDE's - Wavelets or mesh refinement ?,
proceedings of the International Conference of Mathematics (Beijing 2002), 2002.
[C22] F.Arandiga, A. Cohen, M. Doblas, R. Donat and B.Matei,
Sparse representations of images by edge adapted nonlinear multiscale transforms,
IEEE ICIP conference, Barcelona, 2003.
[C23] A. Cohen, Theoretical, applied and computational aspects of
nonlinear approximation in Multiscale problems and methods in numerical
simulation, Lecture Notes in Math 1825, 1-29, Springer, Berlin, 2003.
[C24] J.P. Chehab, A. Cohen, D. Jennequin, J. Nieto, C. Roland and J.-R. Roche,
An adaptive particle-in-cell method using multiresolution analysis,
in Numerical methods for hyperbolic equations, IRMA Lect. Math. Theor. Phys.
Vol. 7, 29-42, Eur. Math. Soc., Zurich, 2005.
[C25] R.Baraniuk, A. Cohen, S. Du, D.B. Johnson and R.Wagner, An Architecture
for Wavelet Analysis and Processing in Sensor Networks,
Proceedings of Information Processing in Sensor Networks, 102-108, 2006.
[C26] P.Binev, A. Cohen, W. Dahmen and R. DeVore, Universal piecewise
polynomial estimators in machine learning, Curves and Surfaces, Avignon,
J.L.Merrien and L.Schumaker eds., 2007.
[C27] A. Cohen, W. Dahmen and R. DeVore, A taste of compressed sensing,
Proc. SPIE, San Diego, 2007.
[C28] A. Cohen, Adaptive approximations by greedy algorithms,
Proc. ICIAM Zurich, 2008.
[C29] A. Cohen, W. Dahmen and R. DeVore, Instance optimal decoding
in compressed sensing, Proceedings El Escorial 08, Contemporary Mathematics 2009.
[C30] A. Cohen and J.-M. Mirebeau, Adaptive finite element approximation,
in Multiscale, Nonlinear and Adaptive Approximation (volume in honor of
Wolfgang Dahmen), Springer, 2009.
[C31] A. Cohen, R. DeVore, S.Foucart and H. Rauhut, Recovery of functions
of many variables via compressed sensing, Proceedings SampTA11, Singapore, 2011.
[C32] A. Cohen, L. Daudet and G. Chardon, Reconstruction of solutions
to the Helmholtz equation from punctual measurements, Proc. SampTA 2013,
Eurasip, 164-167, 2013.
[C33] A. Chkifa, A. Cohen, P.Y. Passagia, J. Peters, A comparative study
between kriging and adaptive sparse tensor-product methods for high-dimensional
approximation and optimization problems in aerodynamics design, ESSAIM Proc 48,
248-261, 2015.
[C34] A. Chkifa and A. Cohen, On the stability of polynomial interpolation using
hierarchical sampling, in Sampling theory - a renaissance, P. Goetz ed, chapter 12,
437-458, Springer, 2016 .
[C35] A. Cohen and G. Migliorati, Multivariate approximation in downward closed polynomial spaces, in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, Vol. I, 533-582,
Springer, 2018.