Analysis of topological derivative as a tool for qualitative identification
Analysis of topological derivative as a tool for qualitative identification
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DOI：
10.1088/1361-6420/ab0b67
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发表时间：
2018-11
期刊：
影响因子：
2.1
通讯作者：
M. Bonnet;F. Cakoni
中科院分区：
文献类型：
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作者：
M. Bonnet;F. Cakoni
拓扑导数的概念已经被证明是一种有效的定性反演工具，用于基于波的有限大小目标识别。尽管在很大程度上，这种方法仍然基于对拓扑导数的启发式解释，但对于具有远场数据和非均匀折射率的各向同性介质的情况，Bellis等人(2013年逆问题29 075012)首次尝试了它的数学证明。本文将这种分析推广到各向异性散射体和近场背景的情况。基于拓扑导数的成像泛函的分析使用了近场的适当因子分解，这要归功于最近在Bonnet(2017 J.积分EQU)中获得的新的体积积分公式。APPL29271-95)。我们的结果包括证明了各向同性主算符跳跃情况下和某些各向异性介质情况下拓扑导数的符号启发式，以及在近场球面测量构型距离探测区域足够远的各向同性情况下验证了其衰变性质。
The concept of topological derivative has proved effective as a qualitative inversion tool for a wave-based identification of finite-sized objects. Although for the most part, this approach remains based on a heuristic interpretation of the topological derivative, a first attempt toward its mathematical justification was done in Bellis et al (2013 Inverse Problems 29 075012) for the case of isotropic media with far field data and inhomogeneous refraction index. Our paper extends the analysis there to the case of anisotropic scatterers and background with near field data. Topological derivative-based imaging functional is analyzed using a suitable factorization of the near fields, which became achievable thanks to a new volume integral formulation recently obtained in Bonnet (2017 J. Integral Equ. Appl. 29 271–95). Our results include justification of sign heuristics for the topological derivative in the isotropic case with jump in the main operator and for some cases of anisotropic media, as well as verifying its decaying property in the isotropic case with near field spherical measurements configuration situated far enough from the probing region.