W. Freeden and U. Windheuser (1996): Spherical Wavelet Transform and its Discretization, Advances in Computational Mathematics, 5, 51-94.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....papers the name PDO is never mentioned but the typical techniques are already used. The introduction of PDOs into Geodesy was done by the famous article [6] and it is nowadays frequently used for the treatment of geodetic boundary value problems [5] and in connection with wavelets on the sphere [1]. ....

Freeden W. and Windheuser U. Spherical wavelet transform and its discretization,Ad- vances in Computational Mathematics 11(1995), pp 1-45

....Let us start with the simplest case, namely the case of the circle, denoted by S 1 . By an abuse of language, we shall sometimes refer to the angular variable 2 S 1 as a periodic time or simply a time variable. Our approach (which is different from that of [4] generalized in [5] and [3] who introduced a notion of scaling adapted to the circle) consists in regarding the circle as a homogeneous space with respect to the action of rotations: given a function f( 2 L 2 ( Gamma; the rotation of angle ff act on it as r ff Delta f( f( Gamma ff) 1) The frequency space ....

W. Freeden, U. Windheuser, Spherical Wavelet Transform and its Discretization, Technical Report N. 125, Technomathematics Dept, University of Kaiserslautern (FRG) (1994).

....0.0 0.2 0.4 0.6 0.8 1.0 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 0.5 Networks Organized by BUD (L=1 4) 171 80 37 14; Total = 302 Fig. 1.1. A global network of 302 weather stations. network of weather stations. A di#erent approach of SW analysis was recently taken by Freeden and Windheuser [12, 13], in which a continuous wavelet transform needs to be approximated by discretization schemes on regular gridpoints. Motivated by data compression for computer graphics, Schroder and Sweldens [27] also proposed an algorithm for SW analysis on the basis of regular gridpoints. Our approach, like that ....

....is to describe a field with components of variable scales. The problem can be attributed to the fact that the SBFs in (2.4) and (2.6) as rotated versions of a single function, have the 934 TA HSIN LI 1 0.5 0 0.5 1 theta (x pi) 0.4 0.2 0 0.2 0. 4 phi (x pi) wavelet Spherical Wavelet (L=2) [12] (ETA=0.6;SDV=0.471) a) 1 0.5 0 0.5 1 theta (x pi) 0.4 0.2 0 0.2 0.4 phi (x pi) 10 wavelet Spherical Wavelet (L=2) 32] ETA=0.6;SDV=0.471) b) Fig. 3.1. Examples of SWs derived by further removing the stations represented by circles in Figure 2.3. a) Wavelet at station 12. b) Wavelet ....

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W. Freeden and U. Windheuser, Spherical wavelet transform and its discretization, Adv. Comput. Math., 5 (1996), pp. 51--94.

....10 ( 6) 24414 3.74 ( 4) 1.39 ( 5) 10 ( 5) 13800 3.10 ( 3) 8.00 ( 5) 10 ( 4) 9745 1.39 ( 2) 4.70 ( 4) 10 ( 3) 8276 5.69 ( 2) 2.83 ( 3) 10 ( 2) 7740 2.69 ( 1) 1.51 ( 2) 10 ( 1) 7668 6.02 ( 1) 3.24 ( 2) Tab. 4. Coefficient errors in Example 2 for selected ffl. we have become aware of the recent work [2,4,8,9,13]. In [2] the authors use tensor splines based on exponential splines in the OE variable. The method in [4] uses discretizations of certain continuous wavelet transforms based on singular integral operators, while the method in [8] uses tensor functions based on polynomials and trigonometric ....

....5.69 ( 2) 2.83 ( 3) 10 ( 2) 7740 2.69 ( 1) 1.51 ( 2) 10 ( 1) 7668 6.02 ( 1) 3.24 ( 2) Tab. 4. Coefficient errors in Example 2 for selected ffl. we have become aware of the recent work [2,4,8,9,13] In [2] the authors use tensor splines based on exponential splines in the OE variable. The method in [4] uses discretizations of certain continuous wavelet transforms based on singular integral operators, while the method in [8] uses tensor functions based on polynomials and trigonometric polynomials. Finally, the method in [9] utilizes C 0 piecewise linear functions defined on spherical ....

Freeden, W. and U. Windheuser, Spherical wavelet transform and its discretization, Adv. Comp. Math. 5 (1996), 51--94.

....( 6) 10 ( 6) 24414 3.74 ( 4) 1.39 ( 5) 10 ( 5) 13800 3.10 ( 3) 8.00 ( 5) 10 ( 4) 9745 1.39 ( 2) 4.70 ( 4) 10 ( 3) 8276 5.69 ( 2) 2.83 ( 3) 10 ( 2) 7740 2.69 ( 1) 1.51 ( 2) 10 ( 1) 7668 6.02 ( 1) 3.24 ( 2) Tab. 4. Coe#cient errors in Example 2 for selected #. we have become aware of the recent work [2,4,8,9,13]. In [2] the authors use tensor splines based on exponential splines in the # variable. The method in [4] uses discretizations of certain continuous wavelet transforms based on singular integral operators, while the method in [8] uses tensor functions based on polynomials and trigonometric ....

....8276 5.69 ( 2) 2.83 ( 3) 10 ( 2) 7740 2.69 ( 1) 1.51 ( 2) 10 ( 1) 7668 6.02 ( 1) 3.24 ( 2) Tab. 4. Coe#cient errors in Example 2 for selected #. we have become aware of the recent work [2,4,8,9,13] In [2] the authors use tensor splines based on exponential splines in the # variable. The method in [4] uses discretizations of certain continuous wavelet transforms based on singular integral operators, while the method in [8] uses tensor functions based on polynomials and trigonometric polynomials. Finally, the method in [9] utilizes C 0 piecewise linear functions defined on spherical ....

Freeden, W. and U. Windheuser, Spherical wavelet transform and its discretization, Adv. Comp. Math. 5 (1996), 51--94.

....every set with twenty one or more points is scattered We hasten to point out that the approach taken here is not limited to the 2 sphere, although that may be where most applications lie. Different approaches to creating wavelets on the 2 sphere have recently been taken by Freeden and Windheuser [11] and by Tasche [26] In [11] a continuous wavelet transform on the sphere is discretized. In [26] one first maps the rectangle [0; Theta [0; 2 ] or box in higher dimensions) to the sphere via standard spherical coordinates, and then one constructs wavelets by taking tensor products of ....

....more points is scattered We hasten to point out that the approach taken here is not limited to the 2 sphere, although that may be where most applications lie. Different approaches to creating wavelets on the 2 sphere have recently been taken by Freeden and Windheuser [11] and by Tasche [26] In [11], a continuous wavelet transform on the sphere is discretized. In [26] one first maps the rectangle [0; Theta [0; 2 ] or box in higher dimensions) to the sphere via standard spherical coordinates, and then one constructs wavelets by taking tensor products of Euclidean wavelets designed for ....

W. Freeden and U. Windheuser, "Spherical Wavelet Transform and its Discretization," Berichte der Arbeitsgruppe Technomathematik von Universitat Kaiserlautern # 125, 1995.

....of wavelets on the sphere was introduced by Dahlke et al. 6] using a tensor product basis where one factor is an exponential spline. To our knowledge a computer implementation of this basis does not exist at this moment. A continuous wavelet transform and its semi discretization were proposed in [13]. Both these approaches make use of a # ; ## parameterization of the sphere. This is the main difference with our method, which is parameterization independent. Aside from being of theoretical interest, a wavelet construction for the sphere leading to efficient algorithms, has practical ....

FREEDEN,W.,AND WINDHEUSER, U. Spherical Wavelet Transform and its Discretization. Tech. Rep. 125, Universit at Kaiserslautern, Fachbereich Mathematik, 1994.

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W. Freeden and U. Windheuser (1996): Spherical Wavelet Transform and its Discretization, Advances in Computational Mathematics, 5, 51-94.

No context found.

W. Freeden, U. Windheuser (1994), Spherical Wavelet Transform and Its Discretization, Berichte der Arbeitsgruppe Technomathematik, Bd. 125, Kaiserslautern

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W. Freeden and U. Windheuser (1996): Spherical Wavelet Transform and its Discretization, Advances in Computational Mathematics, 5, 51-94.

.... interest in wavelet methods on spherical surfaces (cf. e.g. 3] 4] 15] 19] 20] 25] 26] Moreover, a series of papers on spherical wavelets have appeared bringing together essential features of spherical radial basis functions and the concept of axisymmetric wavelets (cf. 12] [13], 14] Wavelet type constructions for, e.g. geophysically more relevant manifolds like ellipsoid, spheroid, geoid, actual (smooth) earth s surface and elliptic partial differential equations, however, have only rudimentarily been attempted and are still in their infancy. Aside from being of ....

....at hand. The P scale discrete wavelets are defined by 0 (x) 0 (x) p ( 1 (x) 2 Gamma ( 0 (x) 2 ; x 2 [0; 1) where the M scale discrete wavelets can be obtained from 0 (x) 1 (x) Gamma 0 (x) x 2 [0; 1) 0 (x) 1 (x) 0 (x) x 2 [0; 1) cf. 12] [13], 14] In both cases it is not difficult to prove that the admissibility condition is satisfied by the generators. 3.4 Examples Besides the conditions of Definition 3.3 there are no further restrictions on the generator 0 . Thus, many choices are at our disposal for application. We first ....

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Freeden, W., Windheuser, U. (1996): Spherical Wavelet Transform and Its Discretization, Adv. Comp. Math., 5, 51-94

....simple pieces at different scales and positions. Basically this is done by convolving the function against rotated and dilated versions of one fixed function, viz. the wavelet Psi. There are at least two ways to introduce wavelets: one is through the continuous wavelet transform (as proposed in [11], 12] another is through the discrete wavelet transform (multiresolution analysis) which is the contents of this paper. In the already known case of continuous wavelet transform the question of complete characterization of a function is answered immediately using the classical continuous ....

....is derived as the simplest example satisfying the orthogonality. Other examples developed from our concept of dilation are the P scale discrete Abel Poisson wavelets, the P scale discrete Gau Weierstra wavelets, both types known from scale discretization of their continuous counterparts (cf. [11], 12] In addition polynomial wavelets, rational and exponential wavelets are mentioned as non band limited examples. An essential aim of scale discrete spherical wavelet transform is to provide an easily interpretable respresentation of square integrable functions on the sphere. The outline of ....

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Freeden, W., Windheuser, U. (1996): Spherical Wavelet Transform and Its Discretization. Advances in Computational Mathematics, 5, 51-94

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W. Freeden, U. Windheuser (1994), Spherical Wavelet Transform and Its Discretization, Berichte der Arbeitsgruppe Technomathematik, Bd. 125, Kaiserslautern

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Freeden, W., Windheuser, U. (1996) Spherical Wavelet Transform and Its Discretization. Adv. Comput. Math., 5, 51-94.

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W. Freeden and U. Windheuser, Spherical Wavelet Transform and Its Discretization, AGTM Report No. 125, University of Kaiserlautern, Geomathematics Group, 1995.

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W. Freeden and U. Windheuser, Spherical Wavelet Transform and Its Discretization, AGTM Report No. 125, University of Kaiserlautern, Geomathematics Group, 1995.

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