A non-linear approximation method on the sphere

被引：9
作者：
Michel V. [1 ]
Telschow R. [1 ]
机构：
[1] Geomathematics Group, Department of Mathematics, University of Siegen, Emmy-Noether-Campus, Walter-Flex-Str. 3, Siegen
来源：
GEM - International Journal on Geomathematics | 2014年 / 5卷 / 2期
关键词：
Greedy algorithm; Matching pursuit; Multiresolution analysis; Non-linear approximation; Regularization; Reproducing kernel; Scaling function; Scattered data; Sphere; Spherical harmonic; Wavelet;
D O I：
10.1007/s13137-014-0063-3
中图分类号：
学科分类号：
摘要：
We show the applicability of a modified version of the recently developed Regularized Functional Matching Pursuit (RFMP) to the approximation of functions on the sphere from grid-based data. We elaborate the mathematical details of the choice of trial functions and the specifics of the algorithm. Moreover, we show numerical examples for some benchmarks. The dictionary of trial functions contains orthogonal polynomials (spherical harmonics) as well as spherical scaling functions and wavelets. It turns out that the greedy algorithm RFMP yields sparse approximations by combining different types of trial functions in a (particular) optimal way, where the sparsity can essentially be increased by a-priori choosing the dictionary appropriately. Moreover, the result of the RFMP can be used for a multiresolution analysis of the investigated function. © 2014, Springer-Verlag Berlin Heidelberg.
引用
收藏
页码：195 / 224
页数：29
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