A frequency based constraint for a multi-frequency linear sampling method
A frequency based constraint for a multi-frequency linear sampling method
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DOI：
10.1088/0266-5611/29/9/095019
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发表时间：
2013-09
期刊：
影响因子：
2.1
通讯作者：
H. Alqadah;Nicolas Valdivia
中科院分区：
文献类型：
--
作者：
H. Alqadah;Nicolas Valdivia
线性采样方法（LSM）已成为一种成熟的非迭代技术，用于各种逆散射问题。该方法提供了一些优势，竞争的逆散射方法，主要是它是基于解决一个线性问题，同时能够考虑多路径效应。不幸的是，在当前框架下，该方法仅在使用大量多静态数据时有效，因此对于许多成像应用可能是不切实际的。虽然主要是在一个单一的频率框架下开发的，最近的方法扩展到多波段数据集已被考虑。通常已知的是，多频率数据的可用性应当补偿减少的空间分集，但是不清楚如何能够针对LSM实现这一点。在这项工作中，我们在这个方向上迈出了一步，考虑基于频率的部分变分方法。我们首先建立的频带上没有任何相应的Dirichlet特征值的Herglotz密度表现出有界变化。然后，我们考虑一个正则化方法，将这种先验知识。所提出的方法表现出一个很好的估计未知的Dirichlet特征值的障碍时，使用减少的数据。这一观察结果也与更高质量的3D重建相关。
The linear sampling method (LSM) has become a well established non-iterative technique for a variety of inverse scattering problems. The method offers a number of advantages over competing inverse scattering methods, mainly it is based on solving a linear problem while being able to account for multi-path effects. Unfortunately under the current framework the method is only effective when using a large number of multi-static data, and therefore may be impractical for many imaging applications. While primarily developed under a single frequency framework, recently the extension of the method to multi-banded data sets has been considered. It is known in general that the availability of multi-frequency data should compensate for reduced spatial diversity, but it is not clear how this can be accomplished for the LSM. In this work we take a step in this direction by considering a frequency based partial variation approach. We first establish that on bands absent of any corresponding Dirichlet eigenvalues the Herglotz density exhibits bounded variation. We then consider a regularization method incorporating this prior knowledge. The proposed approach exhibited a good estimate of the unknown Dirichlet eigenvalues of the obstacle in question when using reduced data. This observation also correlated with higher quality 3D reconstructions.