Approximate weak greedy algorithms

Advances in Computational Mathematics

Volumn 14, Issue 4, 2001, Pages 361-378

  Gribonval, R ^a   Nielsen, M ^b  

^a CAMPUS DE BEAULIEU   (France)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Greedy algorithm; Nonlinear approximation

Indexed keywords

EID: 0035604987     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012255021470     Document Type: Article

References (24)

1. F. Bergeaud, Représentations adaptatives d'images numériques, Matching Pursuit, Ph.D. thesis, Ecole Centrale Paris (1995).
2. F. Bergeaud and S. Mallat, Matching Pursuit: Adaptative representations of images and sounds, Comput. Appl. Math. 15(2) (1996).
3. A. Bultan, A four-parameter atomic decomposition of chirplets, IEEE Trans. Signal Process. 47(3) (1999) 731-745.
4. R.R. Coifman and Y. Meyer, Remarques sur l'analyse de Fourier à fenêtre, C. R. Acad. Sci. Paris Sér. A 312 (1991) 259-261.
5. R.R. Coifman, Y. Meyer, S.R. Quake and M.V. Wickerhauser, Signal processing and compression with wavelet packets, in: Progress in Wavelet Analysis and Applications, eds. Y. Meyer and S. Roques (1992).
6. G. Davis, S. Mallat and M. Avellaneda, Adaptive greedy approximations, Constr. Approx. 13 (1997) 57-98.
7. J.H. Friedman and W. Stuetzle, Projection pursuit regression, J. Amer. Statist. Assoc. 76 (1981) 817-823.
8. R. Gribonval, Approximations non-linéaires pour l'analyse de signaux sonores, Ph.D. thesis, Université Paris IX Dauphine (September 1999).
9. R. Gribonval, Fast matching pursuit with a multiscale dictionary of Gaussian chirps, to appear in IEEE Trans. Signal Process. (May 2001).
10. R. Gribonval, Ph. Depalle, X. Rodet, E. Bacry and S. Mallat, Sound signals decomposition using a high resolution matching pursuit, in: Proc. of Internat. Computer Music Conf. (ICMC'96), August 1996, pp. 293-296.
11. E. Hernández and G. Weiss, A First Course on Wavelets (CRC Press, Boca Raton, FL, 1996).
12. N. Hess-Nielsen and M.V. Wickerhauser, Wavelets and time-frequency analysis, Proc. IEEE 84(4) (1996) 523-540.
13. P.J. Huber, Projection pursuit, Ann. Statist. 13(2) (1985) 435-475.
14. S. Jaggi, W.C. Carl, S. Mallat and A.S. Willsky, High resolution pursuit for feature extraction, J. Appl. Comput. Harmonic Anal. 5(4) (1998) 428-449.
15. L.K. Jones, On a conjecture of Huber concerning the convergence of PP-regression, Ann. Statist. 15 (1987) 880-882.
16. E.D. Livschitz and V.N. Temlyakov, On convergence of weak greedy algorithms, Technical Report 0013, Department of Mathematics, University of South Carolina, Columbia, SC (2000); http://www.math.sc.edu/imip/00papers/0013.ps.
17. S. Mann and S. Haykin, The chirplet transform: Physical considerations, IEEE Trans. Signal Process. 43(11) (1995) 2745-2761.
18. S. Mallat and Z. Zhang, Matching pursuit with time-frequency dictionaries, IEEE Trans. Signal Process. 41(12) (1993) 3397-3415.
19. M.R. McClure and L. Carin, Matching pursuits with a wave-based dictionary, IEEE Trans. Signal Process. 45(12) (1997) 2912-2927.
20. S. Qian and D. Chen, Signal representation using adaptive normalized Gaussian functions, IEEE Trans. Signal Process. 36(1) (1994) 1-11.
21. V.N. Temlyakov, Weak greedy algorithms, Adv. Comput. Math. 12(2,3) (2000) 213-227.
22. V.N. Temlyakov, A criterion for convergence of Weak Greedy Algorithms, Technical Report 0021, Department of Mathematics, University of South Carolina, Columbia, SC (2000); http://ww. math.sc.edu/imip/00papers/0021.ps.
23. B. Torrésani, Wavelets associated with representations of the affine Weyl-Heisenberg group, J. Math. Phys. 32 (May 1991) 1273-1279.
24. M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software (A.K. Peters, 1994).