Brief historical introduction to wavelet transforms

International Journal of Mathematical Education in Science and Technology

Volumn 29, Issue 5, 1998, Pages 677-688

  Debnath, Lokenath ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85007427817     PISSN: 0020739X     EISSN: 14645211     Source Type: Journal    
DOI: 10.1080/0020739980290504     Document Type: Article

References (40)

1. Debnath, L., 1995. Integral Transforms and Their Applications, Boca Raton, FL:CRC Press.
2. Gabor, D., 1946. Theory of communications. J. Inst. Electr. Eng. London, 93:429–457.
3. Glauber, R. J., 1964. Quantum Optics and Electronics, Edited by:de, C., A. Blandin, Witt, and Cohen-Tannoudji, C., New York:Gordon and Breach. Historical.
4. Malvar, H. S., 1990. Lapped transforms for efficient transforms/subband coding. IEEE Trans. ASSP, 38:969–978.
5. Morlet, J., Arens, G., Fourgeau, E., and Giard, D., 1982. Wave propagation and sampling theory, Part I:Complex signal land scattering in multilayer media. J. Geophys., 47:203–221.
6. Morlet, J., Arexs, G., Fourgeau, E., and Giard, D., 1982. Wave propagation and sampling theory and complex waves. J. Geophys., 47:222–236.
7. Grossmann, A., and Morlet, J., 1984. Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal., 15:723–736.
8. Aslaksen, E. W., and Kaluder, J. R., 1968. Unitary representations of the affine group. J. Math Phys., 9(1968):206–211.
9. Aslaksen, E. W., and Kaluder, J. R., 1969. Continuous representation theory using the affine group. J. Math. Phys., 10:2267–2275.
10. Duffin, R. J., and Schaeffer, A. C. 1952. A class of nonharmonic Fourier sereis. Trans. Amer. Math. Soc., 72:341–366.
11. Debnath, L., and Mikusinski, P., 1998. Introduction to Hilbert Spaces with Applications, second ed, Boston:Academic Press.
12. Meyer, Yves. 1990. Ondelettes et opérateurs, Vol. tomes I, II and III, Paris:Herman.
13. Meyer, Yves. 1993. Wavelets, Algorithms and Applications, Edited by:Ryan), Robert D., SIAM Publications.
14. Lemarie, P. G., and Meyer, Y., 1986. Ondelettes et bases hilbertiennnes. Revista Mat. Iberoamer., 2:1–18.
15. Stromberg, J. O., 1982. “ A modified Haar system and higher order spline systems ”. In Conference on Harmonic Analysis in Honor of Antoni Zygmund, II, Wadsworth Math. Series Edited by:Beckner, W., 475–453.
16. Battle, G., 1987. A block spin construction of o?delettes, Part I:Lemarie functions. Commun. Math. Phys., 110:601–615.
17. Le.mariee, P., G., 1988. Ondelettes a localisation exponentielle. J. Math. Pures Appl, 67:227–236.
18. Lemariee, P. G., 1989. Bases d'ondelettes sur les groupes de Lie stratifies. Bull. Soc. Math. France, 117:211–232.
19. Tchamitchan, P., 1987. Biorthogonalité et Théorie des Opérateurs. Revista Matematica, Iberoamericana, 3:163–189.
20. Daubechies, I., Grossmann, A., and Meyer, Y., 1986. Painless nonorthogonal expansion. J. Math Phys., 27:1271–1283.
21. Mallat, S., 1988. Multiresolution representation and wavelets, University of Pennsylvania. PhD Thesis
22. 2(R). Trans. Amer. Math. Soc, 315:69–88.
23. Mallat, S., 1989. A theory for multiresolution signal decomposition:The wavelet representation. IEEE Trans. Patt. Mach. Intell., 11:678–693.
24. Daubechies, I., 1992. Ten Lectures on Wavelets., Philadelphia:SIAM Press. CBMS-NSF Regional Conference Series in Applied Math., 61
25. Daubechies, I., 1988. Orthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math., 41:909–996.
26. Daubechies, I., 1990. The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inform. Theory, 36:951–1005.
27. Burt, P., and Adelson, E., 1983. The Laplacian pyramid as a compact image code. IEEE Trans. Commun., 31:482–540.
28. Burt, P., and Adelson, E., 1983. A multiplication spline with application to image mosaics. ACM Trans. Graphics, 2:217–236.
29. Cohen, A., Daubechies, I., and Feauveau, J., 1992. Biorthogonal basis of compactly supported wavelets. Commun. Pure and Appl. Math., 45:485–560.
30. Cohen, A., 1992. Biorthogonal Wavelets, in Wavelets—A Tutorial in Theory and Applications, 123–152. Academic Press.
31. Chui, C. K., and Wang, J. Z., 1991. A cardinal spline approach to wavelets. Proc. Amer. Math. Soc, 113:785–793.
32. Chui, C. K., and Wang, J. Z., 1992. On compactly supported spline wavelets and a duality principle. Trans. Amer. Math. Soc, 330:903–915.
33. Micehelli, C. 1991. Using the refinement equation for the construction of prewavelets. Numer. Alg., 1:75–116.
34. Holschneider, M., 1988. L'analyse d'objets fractals et leur transformaé en ondelettes, Marseille:Thèse, Université de Provence.
35. Holschxeider, M., and Tchamitchian, P., 1991. Pointwise regularity of Riemann's “non-differentiable” function. Invent. Math., 105:157–175.
36. Beylkin, G., Coifman, R., and Rokhlin, V., 1991. Fast wavelet transforms and numerical algorithms. Commun. Pure Appl. Math., 44:141–183.
37. Beylkin, G., 1992. On the representation of operators in bases of compactly supported wavelets. SIAM J. Numer. Anal, 29:1716–1740.
38. Coifman, R. R., Meyer, Y., and Wickerhauser, M. V., 1992. “ Wavelet analysis and signal processing ”. In Wavelets and Their Applications, Edited by:Ruskai. 153–178. Boston:Jones and Bartlett.
39. Coifman, R. R., Meyer, Y., and Wickerhauser, M. V., 1992. “ Size properties of wavelet packets ”. In Wavelets and Their Applications, Edited by:Ruskai. 453–470. Boston:Jones and Bartlett.
40. 2boundedness of Cauchy integrals on Lipschitz curves. J. Amer. Math. Soc, 2:553–564.