Wavelets and Functions with Bounded Variation from Image Processing to Pure Mathematics
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. S1, pp. 77-105.

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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.
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Meyer, Yves. Wavelets and Functions with Bounded Variation from Image Processing to Pure Mathematics. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. S1, pp. 77-105. http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_S1_a5/

[1] A. Bonami - S. Poornima, Non-multipliers of Sobolev spaces. Journ. Funct. Anal., 71, 1987, 175-181. | DOI | MR | Zbl

[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 | Zbl

[4] I. Daubechies, Ten lectures on wavelets. SIAM, Philadelphia 1992. | DOI | MR | Zbl

[5] R. Devore - B. Jawerth - V. Popov, Compression of wavelet decompositions. American Journal of Mathematics, 114, 1992, 737-785. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[8] D. Donoho - I. Johnstone, Wavelet shrinkage: Asymptopia? J. R. Statist. Soc., B, 57 (2), 1995, 301-369. | MR | Zbl

[9] J.-P. Kahane - P.-G. Lemarié-Rieusset, Fourier Series and Wavelets. Gordon and Breach Science Publishers, 1996. | MR

[10] S. Mallat, A Wavelet Tour of Signal Processing. Academic Press, 1998. | MR | Zbl

[11] Y. Meyer, Wavelets, Algorithms & Applications. SIAM, Philadelphia 1993. | MR

[12] Y. Meyer, Wavelets and Operators. Cambridge studies in advanced mathematics, 37 CUP, 1992. | MR

[13] Y. Meyer, Wavelets, vibrations and scalings. CRM Monograph Series, vol. 9, 1998. | MR | Zbl

[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.