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. 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, "Regularite 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 functionin 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 approximatio 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", IMAVIS 28, 553-562, 2010. 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 wavele 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. IV. UNPUBLISHED REPORTS [R1] A.Bruckstein, A.Cohen and G.Shapiro, "A subdivision for continuous B-splines and affine-invariant progressive smoothing", rapport CEREMADE 1994. [R2] A.Cohen, N.Dyn and D.Levin, "Matrix subdivision schemes", rapport LAN 1997. [R3] A.Averbuch, A.Cohen and M.Israeli, "A fast and accurate multiscale scheme for parabolic equations", rapport LAN 1998. [R4] A.Cohen, L-M.Echeverry and Q.Sun, "Finite element wavelets", rapport LAN, 1999. V. SUBMITTED [E1] A. Cohen, N. Dyn, F. Hecht and J.-M. Mirebeau, "Adaptive multiresolution analysis based on anisotropic triangulations", submitted to Math. of Comp, 2009. [E2] A. Cohen and J.-M. Mirebeau, "Greedy bisection generates optimally adapted triangulations", submitted to Math. of Comp, 2009. [E3] A.Cohen, R. DeVore and C. Schwab, "Nonlinear approximation of stochatic PDEÕs", submitted to J. of the AMS., 2009. [E4] A. Cohen and J.M. Mirebeau, "Anisotropic smoothness classes : from finite element approximation to image models", submitted to J. Math. Imaging and Vision, 2009. [E5] A. Cohen and H. Bahouri, "Refined Sobolev inequalities in Lorenz spaces", submitted to J. Fourier Anal. and Appl. 2010. [E6] A. Cohen, R. DeVore and C. Schwab, "Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs", preprint, 2010 .