Abstract:
In this paper we propose an extended family of almost orthogonal spline wavelets with compact support. These functions provide snug bases for L2 (ℛ), preserving semiorthogonal properties. As it is well known, orthogonality is a desirable quality while finite support has attractive features for numerical applications. This work represents an effort to combine these conditions in the spline case and to enhance previous results of Chui and Unser et al. We start by reviewing the concept of semiorthogonal wavelets and we discuss their performance. Next, we give a brief description of the general technique for computing compactly supported spline wavelets. Finally we expose these functions. We also develop several formulas in accord with our purposes. © 1996 Academic Press, Inc.
Referencias:
- Ahlberg, J.M., Nilson, E.N., Walsh, J.L., (1967) The Theory of Splines and Their Applications, , Academic Press, New York
- Battle, G., A block spin construction of ondelettes. Part I: Lemarié functions (1987) Comm. Math. Phys., 110, pp. 601-615
- Chui, C.K., (1991) Multivariate Splines, , SIAM, Philadelphia
- Chui, C.K., (1992) An Introduction to Wavelets, , Academic Press, Boston
- Daubechies, I., Orthonormal bases of compactly supported wavelets (1988) Comm. Pure Appl. Math., 41, pp. 909-996
- Daubechies, I., (1992) Ten Lectures on Wavelets, , SIAM, Philadelphia
- Heil, C.E., Walnut, D.F., Continuous and discrete wavelet transforms (1989) SIAM Rev., 31, pp. 628-666
- Lemarié, P.G., Une nouvelle base d'ondelettes de L2 (ℛn) (1988) J. Math. Pure Appl., 67, pp. 227-236
- Mallat, S., A theory of multiresolution signal decomposition: The wave let representation (1989) IEEE Trans. Pattern Anal. Machine Intell., 11, pp. 674-693
- Mallat, S., Multiresolution approximations and wavelet orthonormal bases of L2(ℛ) (1989) Trans. Amer. Math. Soc., 315, pp. 69-87
- Meyer, Y., Ondelettes, fonctions splines et analyses graduees (1987) Rend. Sem. Mat. Univers. Politecn. Torino, 45. , Torino
- Meyer, Y., Wavelets and operators (1989) Cahiers de Mathematiques de la Decision, 8704. , CEREMADE, Universite de Paris Dauphine, Paris
- Meyer, Y., Wavelets and applications (1990) Proceedings of the International Congress of Mathematicians, pp. 1621-1626. , Kyoto
- Meyer, Y., (1990) Ondelettes et Operateurs. I. Ondelettes, , Hermann, Paris
- Meyer, Y., (1993) Wavelets: Algorithms & Applications, , SIAM, Philadelphia
- Meyer, Y., Book Reviews (1993) Bull. Amer. Math. Soc., 28, pp. 350-360
- Powell, M.J., (1981) Approximation Theory and Methods, , Cambridge Univ. Press, Cambridge, U. K
- Schoenberg, I.J., (1993) Cardinal Spline Interpolation, , SIAM, Philadelphia
- Unser, M., Aldroubi, A., Eden, M., A family of polynomial spline wavelet transforms (1993) Signal Process, 30, pp. 141-162
- Usner, M., Aldroubi, A., Eden, M., B-spline signal processing: Part I-theory (1993) IEEE Trans. Signal Process, 41, pp. 821-833
- Unser, M., Aldroubi, A., Eden, M., B-spline signal processing: Part II-efficient design and applications (1993) IEEE Trans. Signal Process, 41, pp. 835-847
- Vetterli, M., Filter banks allowing perfect reconstruction (1986) Signal Process, 10, pp. 219-244
- Wahba, G., (1990) Spline Models for Observational Data, , SIAM, Philadelphia
Citas:
---------- APA ----------
(1996)
. Some remarks about compactly supported spline wavelets. Applied and Computational Harmonic Analysis, 3(1), 57-64.
http://dx.doi.org/10.1006/acha.1996.0004---------- CHICAGO ----------
Serrano, E.P.
"Some remarks about compactly supported spline wavelets"
. Applied and Computational Harmonic Analysis 3, no. 1
(1996) : 57-64.
http://dx.doi.org/10.1006/acha.1996.0004---------- MLA ----------
Serrano, E.P.
"Some remarks about compactly supported spline wavelets"
. Applied and Computational Harmonic Analysis, vol. 3, no. 1, 1996, pp. 57-64.
http://dx.doi.org/10.1006/acha.1996.0004---------- VANCOUVER ----------
Serrano, E.P. Some remarks about compactly supported spline wavelets. Appl Comput Harmonic Anal. 1996;3(1):57-64.
http://dx.doi.org/10.1006/acha.1996.0004