Analysis of the linear sampling method for imaging penetrable obstacles in the time domain
Analysis of the linear sampling method for imaging penetrable obstacles in the time domain
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DOI：
10.2140/apde.2021.14.667
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发表时间：
2021-05
期刊：
影响因子：
2.2
通讯作者：
F. Cakoni;P. Monk;V. Selgás
中科院分区：
文献类型：
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作者：
F. Cakoni;P. Monk;V. Selgás
我们考虑通过因果波的时域测量来定位和重建可穿透障碍物的几何形状的问题。更准确地说，我们假设由于放置在包围障碍物的表面上的点源而给出了散射场，并且散射场是在同一表面上测量的。我们希望根据这些多静态散射数据确定目标的位置和形状。为了处理这个逆问题，我们通过在傅里叶拉普拉斯域中定位内部传输特征值，提出并分析了时域线性采样方法（TDLSM）。我们还证明了前向问题和内部传输问题的新时域估计，并分析了反演方案中出现的几个时域算子。
We consider the problem of locating and reconstructing the geometry of a penetrable obstacle from time domain measurements of causal waves. More precisely, we assume that we are given the scattered field due to point sources placed on a surface enclosing the obstacle, and that the scattered field is measured on the same surface. From these multi-static scattering data we wish to determine the position and shape of the target. To deal with this inverse problem, we propose and analyze the Time Domain Linear Sampling Method (TDLSM) by means of localizing the interior transmission eigenvalues in the FourierLaplace domain. We also prove new time domain estimates for the forward problem and the interior transmission problem, as well as analyze several time domain operators arising in the inversion scheme.