A non-linear approximation method on the sphere
A non-linear approximation method on the sphere
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DOI：
10.1007/s13137-014-0063-3
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
V. Michel;R. Telschow
中科院分区：
文献类型：
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作者：
V. Michel;R. Telschow
我们显示了最近开发的正则函数匹配追踪（RFMP）的修改版本的适用性，从基于网格的数据的球体上的函数的近似。我们详细阐述了试验函数的选择和算法的具体细节的数学细节。此外，我们展示了一些基准的数值例子。试函数字典包含正交多项式（球面调和函数）以及球面尺度函数和小波。事实证明，贪婪算法RFMP通过以（特定）最优方式组合不同类型的试验函数来产生稀疏近似，其中稀疏性可以通过先验地适当选择字典来基本上增加。此外，RFMP的结果可用于所研究函数的多分辨率分析。
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.