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Referenza completa

Meyer, Yves:
Wavelets and Functions with Bounded Variation from Image Processing to Pure Mathematics
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 11 (2000), fasc. n.S1 —Mathematics Towards The Third Millenium, p. 77-105, (English)
pdf (1.23 MB), djvu (3.71 MB). | MR 1845666 | Zbl 1149.42309

Sunto

JPEG-2000 has the potential to be the most significant advance in still image compression since the introduction of JPEG over a decade ago. JPEG-2000 is a wavelet based algorithm and it relies on new estimates on wavelet coefficients of functions of bounded variation. These new estimates have far reaching implications in pure mathematics.
Referenze Bibliografiche
[1] A. BONAMI - S. POORNIMA, Non-multipliers of Sobolev spaces. Journ. Funct. Anal., 71, 1987, 175-181. | fulltext (doi) | MR 879706 | Zbl 0627.46034
[2] CH. M. BRISLAW, Fingerprints go digital. Notices of the AMS, vol. 42, no. 11, nov. 1995, 1278-1283. http://www.c3. lanl. gov/ brislawn
[3] A. COHEN - R. DEVORE - P. PETRUSHEV - H. XU, Nonlinear approximation and the space $BV (\mathbb{R}^{2})$. American Journal of Mathematics, 121, 1999, 587-628. | MR 1738406 | Zbl 0931.41019
[4] I. DAUBECHIES, Ten lectures on wavelets. SIAM, Philadelphia 1992. | fulltext (doi) | MR 1162107 | Zbl 0776.42018
[5] R. DEVORE - B. JAWERTH - V. POPOV, Compression of wavelet decompositions. American Journal of Mathematics, 114, 1992, 737-785. | fulltext (doi) | MR 1175690 | Zbl 0764.41024
[6] R. DEVORE - B. J. LUCIER, Fast wavelet techniques for near optimal image compression. IEEE Military Communications Conference (October 11-14, 1992).
[7] D. DONOHO, Nonlinear Solution of Linear Inverse Problems by Wavelet-Vaguelette Decomposition. Applied and Computational Harmonic Analysis, 2, 1995, 101-126. | fulltext (doi) | MR 1325535 | Zbl 0826.65117
[8] D. DONOHO - I. JOHNSTONE, Wavelet shrinkage: Asymptopia? J. R. Statist. Soc., B, 57 (2), 1995, 301-369. | MR 1323344 | Zbl 0827.62035
[9] J.-P. KAHANE - P.-G. LEMARIÉ-RIEUSSET, Fourier Series and Wavelets. Gordon and Breach Science Publishers, 1996. | MR 3585499
[10] S. MALLAT, A Wavelet Tour of Signal Processing. Academic Press, 1998. | MR 1614527 | Zbl 0937.94001
[11] Y. MEYER, Wavelets, Algorithms & Applications. SIAM, Philadelphia 1993. | MR 1219953
[12] Y. MEYER, Wavelets and Operators. Cambridge studies in advanced mathematics, 37 CUP, 1992. | MR 1228209
[13] Y. MEYER, Wavelets, vibrations and scalings. CRM Monograph Series, vol. 9, 1998. | MR 1483896 | Zbl 0893.42015
[14] J.-M. MOREL, Filtres itératifs des images et équations aux dérivées partielles. Notes de cours du centre Emile Borel, 1998.
[15] J.-M. MOREL - S. SOLIMINI, Variational methods in image segmentation. Birkhäuser, Boston 1995.
[16] D. MUMFORD, Book reviews on [12]. Bulletin of the American Mathematical Society, vol. 33, n. 2, April 1996.
[17] D. MUMFORD - J. SHAH, Boundary detection by minimizing functionals. Proc. IEEE Conf. Comp. Vis. Pattern Recognition, 1985.
[18] F. ORU, Le rôle des oscillations dans quelques problèmes d'analyse non-linéaire. Thèse, CMLA, Ecole Norm. Sup. de Cachan, 9 Juin 1998.
[19] L. RUDIN - S. OSHER, Total variation based image restoration with free local constraints. Proceedings Intern. Conf. on Image Processing (Austin, 1994). IEEE Press, Piscataway, N.J., 1994, 31-35.

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