Fast Wavelet Transform by Biorthogonal Locally Supported Radial Basis Functions on Fixed Spherical Grids

  • The thesis is concerned with multiscale approximation by means of radial basis functions on hierarchically structured spherical grids. A new approach is proposed to construct a biorthogonal system of locally supported zonal functions. By use of this biorthogonal system of locally supported zonal functions, a spherical fast wavelet transform (SFWT) is established. Finally, based on the wavelet analysis, geophysically and geodetically relevant problems involving rotation-invariant pseudodifferential operators are shown to be efficiently and economically solvable.

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Author:Ali A. Moghiseh
URN (permanent link):urn:nbn:de:hbz:386-kluedo-21642
Advisor:W. Freeden
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2007
Year of Publication:2007
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2007/12/21
Tag:Biorthogonalisation ; Locally Supported Zonal Kernels ; Multiresolution Analysis; Radial Basis Functions ; Spherical Fast Wavelet Transform
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):41A30 Approximation by other special function classes
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
44A35 Convolution
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35]
65D15 Algorithms for functional approximation
65T60 Wavelets
86A04 General

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