Study on Parameter Choice Methods for the RFMP with Respect to Downward Continuation
Study on Parameter Choice Methods for the RFMP with Respect to Downward Continuation
复制标题
向下延续的RFMP参数选择方法研究
DOI：
10.3389/fams.2017.00010
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
R. Telschow
中科院分区：
文献类型：
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作者：
M. Gutting;Bianca Kretz;V. Michel;R. Telschow
最近，正则化函数匹配追踪（RFMP）被引入作为线性不适定反问题的贪婪算法。该算法结合了Tikhonov-Phillips正则化，这意味着参数选择的必要性。在本文中，一些已知的参数选择方法的RFMP及其增强，正则化正交函数匹配追踪（ROFMP）的性能进行评估。作为线性反问题的一个例子，重力场数据从卫星轨道向下延拓到地球表面被选择，因为它是指数不适定的。对于测试场景，不同的卫星高度与几个噪声信号比和各种噪声相结合。在这些情况下的参数选择策略的性能进行了分析。例如，它表明，一个强烈分散的数据点集是一个本质上更难的挑战，比一个规则的网格的正则化。所得到的结果产生的第一个方向，参数选择方法是可行的RFMP和ROFMP。
Recently, the regularized functional matching pursuit (RFMP) was introduced as a greedy algorithm for linear ill-posed inverse problems. This algorithm incorporates the Tikhonov-Phillips regularization which implies the necessity of a parameter choice. In this paper, some known parameter choice methods are evaluated with respect to their performance in the RFMP and its enhancement, the regularized orthogonal functional matching pursuit (ROFMP). As an example of a linear inverse problem, the downward continuation of gravitational field data from the satellite orbit to the Earth's surface is chosen, because it is exponentially ill-posed. For the test scenarios, different satellite heights with several noise-to-signal ratios and kinds of noise are combined. The performances of the parameter choice strategies in these scenarios are analyzed. For example, it is shown that a strongly scattered set of data points is an essentially harder challenge for the regularization than a regular grid. The obtained results yield a first orientation which parameter choice methods are feasible for the RFMP and the ROFMP.
正则化函数匹配追踪（RFMP）算法的收敛定理
DOI：
10.1007/s13137-017-0095-6
发表时间：
2017
期刊：
GEM - International Journal on Geomathematics
影响因子：
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作者：
V. Michel;S. Orzlowski
通讯作者：
S. Orzlowski