论文标题
词典学习添加 - 用于向下延续的词典
A dictionary learning add-on for spherical downward continuation
论文作者
论文摘要
我们为现有的近似算法提出了一种新型的词典学习附加组件，用于球形反问题，例如重力势的向下延续。逆问题匹配追踪（IPMP）算法迭代将Tikhonov功能最小化，以构建所谓的词典元素的加权线性组合作为正则化近似。字典是包含试验函数的集合，例如球形谐波（SHS），SLEPIAN函数（SLS）以及径向基函数（RBFS）和小波（RBWS）。以前，IPMP算法与有限词典合作，这些词典在可能的结果偏见方面很容易受到攻击。在这里，我们提出了一种额外的学习技术，该技术使我们能够无限地使用许多试验功能，并为我们提供了一个学到的词典，用于IPMP算法中的未来使用。我们解释了一般机制，并提供了证明其适用性和效率的数值结果。
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.
