C. Bennett and R. Sharpley, Interpolation of Operators, 1988.

A. Cohen, W. Dahmen, I. Daubechies, and R. Devore, Tree Approximation and Optimal Encoding, Applied and Computational Harmonic Analysis, vol.11, issue.2, pp.192-226, 2001.
DOI : 10.1006/acha.2001.0336
URL : http://doi.org/10.1006/acha.2001.0336

O. Christensen, An introduction to frames and Riesz bases (Applied Numerical Harmonic Analysis), 2003.

R. R. Coifman and Y. Meyer, Remarques sur l'analyse de Fourier à fenêtre, Comptes-Rendus Acad. Sci. Paris (A) C. R. Acad. Sci. Paris (Sér. I), vol.312, issue.312, pp.259-261, 1991.

A. Cohen, Biorthogonal wavelets, in Wavelets: A Tutorial in Theory and, pp.123-152, 1992.

R. A. Devore, Nonlinear approximation This is the author version of an article published in a Springer journal. The original publication is available at springerlink.com with DOI: 10, Acta Numerica, pp.51-150, 1007.

I. Daubechies, B. Han, A. Ron, and Z. Shen, Framelets: MRA-based constructions of wavelet frames, Applied and Computational Harmonic Analysis, vol.14, issue.1, 2001.
DOI : 10.1016/S1063-5203(02)00511-0

I. Daubechies, S. Jaffard, and J. L. Journé, A Simple Wilson Orthonormal Basis with Exponential Decay, SIAM Journal on Mathematical Analysis, vol.22, issue.2, pp.554-572, 1991.
DOI : 10.1137/0522035

R. A. Devore, B. Jawerth, and V. Popov, Compression of Wavelet Decompositions, American Journal of Mathematics, vol.114, issue.4, pp.737-785, 1992.
DOI : 10.2307/2374796

S. J. Dilworth, N. J. Kalton, D. Kutzarova, and V. N. Temlyakov, The Thresholding Greedy Algorithm, Greedy Bases, and Duality, Constructive Approximation, vol.19, issue.4, pp.575-597, 2003.
DOI : 10.1007/s00365-002-0525-y

R. A. Devore and G. G. Lorentz, Constructive Approximation, 1993.

G. Davis, S. Mallat, and M. Avellaneda, Adaptive greedy approximations, Constructive Approximation, vol.21, issue.1, pp.57-98, 1997.
DOI : 10.1007/BF02678430
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.7530

R. A. Devore and V. N. Temlyakov, Some remarks on greedy algorithms, Advances in Computational Mathematics, vol.102, issue.1, pp.173-187, 1996.
DOI : 10.1007/BF02124742

H. G. Feichtinger, Modulation spaces on locally compact abelian groups, 1983.

J. H. Friedman and J. W. Tukey, A Projection Pursuit Algorithm for Exploratory Data Analysis, IEEE Transactions on Computers, vol.23, issue.9, pp.881-889, 1974.
DOI : 10.1109/T-C.1974.224051

B. Golubov, A. Efimov, and V. Skvortsov, Walsh Series and Transforms, Theory and Applications, Translated from the 1987 Russian original by, 1991.

R. Gribonval and M. Nielsen, Some remarks on nonlinear approximation with Schauder bases, East J. Approx, vol.7, issue.3, pp.267-285, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00576640

R. Gribonval and M. Nielsen, Nonlinear Approximation with Dictionaries. II. Inverse Estimates, Constructive Approximation, vol.24, issue.2, 2002.
DOI : 10.1007/s00365-005-0621-x
URL : https://hal.archives-ouvertes.fr/inria-00564480

R. Gribonval and M. Nielsen, On approximation with spline generated framelets, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00567338

K. Gröchenig, Foundations of Time-Frequency Analysis (Applied Numerical and Harmonic Analysis ), 2001.

K. Gröchenig and S. Samarah, Nonlinear Approximation with Local Fourier Bases, Constructive Approximation, vol.16, issue.3, pp.317-332, 2000.
DOI : 10.1007/s003659910014

P. J. Huber, Projection Pursuit, The Annals of Statistics, vol.13, issue.2, pp.435-475, 1985.
DOI : 10.1214/aos/1176349519

L. K. Jones, On a conjecture of Huber concerning the convergence of PP-regression, pp.880-882, 1987.

L. K. Jones, A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network Training, The Annals of Statistics, vol.20, issue.1, pp.608-613, 1992.
DOI : 10.1214/aos/1176348546

L. K. Jones, The computational intractability of training sigmoidal neural networks, IEEE Transactions on Information Theory, vol.43, issue.1, pp.167-173, 1997.
DOI : 10.1109/18.567673

K. Kerkyacharian and D. Picard, Entropy, Universal Coding, Approximation, and Bases Properties, Constructive Approximation, vol.20, issue.1, 2001.
DOI : 10.1007/s00365-003-0556-z
URL : https://hal.archives-ouvertes.fr/hal-00102265

S. V. Konyagin and V. N. Temlyakov, A remark on greedy approximation in Banach spaces, East J. Approx, vol.5, issue.3, pp.365-379, 1999.

J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, 1979.
DOI : 10.1007/978-3-662-35347-9

S. Mallat, A Wavelet Tour of Signal Processing, 1998.

Y. Meyer, Wavelets and Operators, 1990.

G. Pisier, Remarques sur un résultat non publié de B. Maurey, in Seminar on Functional Analysis, Exp. No. V, 13. École Polytech, 1980.

W. Pompe, ), Colloquium Mathematicum, vol.92, issue.1, pp.19-34, 2002.
DOI : 10.4064/cm92-1-2

A. Ron and Z. Shen, Affine systems in L 2 (R d ), II: Dual systems, J. Fourier Anal. Appl, vol.3, issue.5, pp.618-637, 1997.

A. Ron and Z. Shen, Affine Systems inL2(Rd): The Analysis of the Analysis Operator, Journal of Functional Analysis, vol.148, issue.2, pp.408-447, 1997.
DOI : 10.1006/jfan.1996.3079

S. Samarah, Approximation theory and modulation spaces This is the author version of an article published in a Springer journal. The original publication is available at springerlink.com with DOI: 10, pp.41-45, 1007.

S. B. Stechkin, On absolute convergence of orthogonal series, Dok. Akad Greedy algorithms in Banach spaces, Nauk SSSR Adv. Comput. Math, vol.102, issue.143, pp.37-40, 1955.

V. N. Temlyakov and H. P. Triebel, Nonlinear methods of approximation, Found Theory of Function Spaces Greedy algorithm for general biorthogonal systems, Wavelets as unconditional bases in L p (R), pp.33-107, 1983.

I. and C. Beaulieu, F-35042 Rennes cedex, France e-mail: remi.gribonval@inria