Spherical wavelet transform and its discretization

被引：77

作者：

Freeden, W ^{[1
]}

Windheuser, U ^{[1
]}

机构：

[1] UNIV KAISERSLAUTERN,LAB TECHNOMATH,GEOMATH GRP,D-67663 KAISERSLAUTERN,GERMANY

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 1996年 / 5卷 / 01期

关键词：

spherical continuous wavelet transform; scale discretizations; wavelet packets; Daubechies wavelets; (R-)multiresolution analysis;

D O I：

10.1007/BF02124735

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A continuous version of spherical multiresolution is described, starting from continuous wavelet transform on the sphere. Scale discretization enables us to construct spherical counterparts to wavelet packets and scale discrete wavelets. The essential tool is the theory of singular integrals on the sphere. It is shown that singular integral operators forming a semigroup of contraction operators of class (C-0) (like Abel-Poisson or Gau ss-Weierstra ss operators) lead in a canonical way to (pyramidal) algorithms.

引用

页码：51 / 94

页数：44

共 17 条

[1] Berens H., 1968, PUBL RES I MATH SCI, V4, P201
[2] Calderon A.-P., 1964, Studia Math., V24, P113, DOI DOI 10.4064/SM-24-2-113-190
[3] CALDERON AP, 1955, T AM MATH SOC, V78, P205
[4] Chui C.K., 1992, An introduction to wavelets, V1, DOI DOI 10.1109/99.388960
[5] DAHLKE S, 1994, CONTINUOUS WAVELET T
[6] THE WAVELET TRANSFORM, TIME-FREQUENCY LOCALIZATION AND SIGNAL ANALYSIS
DAUBECHIES, I
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1990, 36 (05) : 961 - 1005
[7] Daubechies I., 1992, CBMS NSF SERIES APPL, V61
[8] CONTINUOUS WAVELET DECOMPOSITIONS, MULTIRESOLUTION, AND CONTRAST ANALYSIS
DUVALDESTIN, M
MUSCHIETTI, MA
TORRESANI, B
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (03) : 739 - 755
[9] NONORTHOGONAL EXPANSIONS ON THE SPHERE
FREEDEN, W
SCHREINER, M
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1995, 18 (02) : 83 - 120
[10] FREEDEN W, 1979, UBER KLASSE INTEGRAL

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