一个用于球面向下延拓的字典学习插件
A dictionary learning add-on for spherical downward continuation
摘要：
我们提出了一种新的字典学习附加的球形逆问题，如向下延续的引力势的现有近似算法。逆问题匹配追踪（IPMP）算法迭代地最小化Tikhonov泛函，以便构造所谓的字典元素的加权线性组合作为正则化近似。字典是包含测试函数的集合，所述测试函数诸如球谐函数（SH）、Slepian函数（SL）以及径向基函数（RBF）和小波（RBW）。以前，IPMP算法与有限的字典，这是脆弱的关于可能的偏差的结果。在这里，我们提出了一个额外的学习技术，使我们能够与无限多的测试函数，并为我们提供了一个学习字典，供将来使用的IPMP算法。我们解释的一般机制，并提供数值结果证明其适用性和效率。
英文摘要：
We propose a novel dictionary learning add-on for existing approximation algorithms for spherical inverse problems such as the downward continuation of the gravitational potential. The Inverse Problem Matching Pursuit (IPMP) algorithms iteratively minimize the Tikhonov functional in order to construct a weighted linear combination of so-called dictionary elements as a regularized approximation. A dictionary is a set that contains trial functions such as spherical harmonics (SHs), Slepian functions (SLs) as well as radial basis functions (RBFs) and wavelets (RBWs). Previously, the IPMP algorithms worked with finite dictionaries which are vulnerable regarding a possible biasing of the outcome. Here, we propose an additional learning technique that allows us to work with infinitely many trial functions and provides us with a learnt dictionary for future use in the IPMP algorithms. We explain the general mechanism and provide numerical results that prove its applicability and efficiency.
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