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首页> 外文期刊>IEEE Transactions on Geoscience and Remote Sensing. >Inverse Source Problem for a Host Medium Having Pointlike Inhomogeneities
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Inverse Source Problem for a Host Medium Having Pointlike Inhomogeneities

机译：具有点状不均匀性的宿主介质的逆源问题

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摘要

The reconstruction of a source embedded within a multipath environment, which is created by inserting a grid of point scatterers in the scene, is addressed. In particular, the source Fourier spectrum is assumed known so that the focus here is on the reconstruction of the spatial support. As well documented, multipath can allow for resolution improvement. However, it also gives rise to artifacts when a backpropagation-like imaging is adopted. In this paper, we study in detail how resolution improvement and artifacts depend on the grid layout by employing a weighted backpropagation algorithm. More in detail, stationary phase arguments are used to predict the reconstruction leading order terms to which resolution improvement is linked. Moreover, it is shown that artifacts are mainly due to high-order terms and are dependent on the point scatterers’ arrangement. The nature of such artifacts is studied, and a simple way to mitigate their role (without resolution loss) is introduced; it consists in a suitable nonuniform grid arrangement with a “hole in the center.” Backpropagation is then compared with an inverse filtering imaging based on the truncated singular value decomposition (TSVD) of the radiation operator. It is shown that the TSVD is less prone to artifacts and can, in principle, allow for a higher resolution improvement. However, when model error (due to multiple scattering between the elements of the grid) and/or noise corrupt data, backpropagation performs definitely better. The theoretical findings are supported by an extensive numerical analysis. In particular, to keep the figures simple, we consider only 2-D cases.
机译：解决了在多路径环境中嵌入的源的重构，该重构是通过在场景中插入点散射体网格来创建的。特别地，假定源傅立叶谱是已知的，因此这里的重点是空间支持的重建。有据可查，多路径可以提高分辨率。但是，当采用类似反向传播的成像方法时，也会引起伪像。在本文中，我们通过使用加权反向传播算法来详细研究分辨率提高和伪影如何取决于网格布局。更详细地讲，固定相位自变量用于预测与分辨率提高相关联的重构先导项。此外，结果表明，伪影主要是由于高阶项引起的，并且取决于点散射体的排列。研究了此类伪像的性质，并介绍了减轻其作用的简单方法（不降低分辨率）；它由合适的不均匀网格排列组成，并带有“中心孔”。然后将反向传播与基于辐射算子的截断奇异值分解（TSVD）的逆滤波成像进行比较。结果表明，TSVD不太容易出现伪像，并且原则上可以实现更高的分辨率。但是，当模型错误（由于网格元素之间存在多次散射）和/或噪声破坏了数据时，反向传播的性能肯定更好。理论发现得到广泛的数值分析的支持。特别是，为了使图简单，我们仅考虑二维情况。

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