Analysis of the linear sampling method for imaging penetrable obstacles in the time domain

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-18 DOI:10.2140/APDE.2021.14.667

F. Cakoni, P. Monk, V. Selgás

引用次数: 11

Abstract

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.

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可穿透障碍物时域成像的线性采样方法分析

我们考虑了根据因果波的时域测量来定位和重建可穿透障碍物的几何结构的问题。更准确地说，我们假设我们得到了由于点源放置在包围障碍物的表面上而产生的散射场，并且散射场是在同一表面上测量的。根据这些多静态散射数据，我们希望确定目标的位置和形状。为了解决这个逆问题，我们提出并分析了时域线性采样方法（TDLSM），通过将内部传输特征值定位在FourierLaplace域中。我们还证明了前向问题和内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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.