Hohage, Thorsten
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Hohage, Thorsten
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Hohage, Thorsten
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Item-typ:Veröffentlichung, Effective and Efficient Reconstruction Schemes for the Inverse Medium Problem in Scattering(2019-08-19); ; ; This thesis challenges with the development of a computational framework facilitating the solution for the inverse medium problem in time-independent scattering in two- and three-dimensional setting. This includes three main application cases: the simulation of the scattered field for a given transmitter-receiver geometry; the generation of simulated data as well as the handling of real-world data; the reconstruction of the refractive index of a penetrable medium from several measured, scattered fields. We focus on an effective and efficient reconstruction algorithm. Therefore we set up a variational reconstruction scheme. The underlying paradigm is to minimize the discrepancy between the predicted data based on the reconstructed refractive index and the given data while taking into account various structural a priori information via suitable penalty terms, which are designed to promote information expected in real-world environments. Finally, the scheme relies on a primal-dual algorithm. In addition, information about the obstacle's shape and position obtained by the factorization method can be used as a priori information to increase the overall effectiveness of the scheme. An implementation is provided as MATLAB toolbox IPscatt. It is tailored to the needs of practitioners, e.g. a heuristic algorithm for an automatic, data-driven choice of the regularization parameters is available. The effectiveness and efficiency of the proposed approach are demonstrated for simulated as well as real-world data by comparisons with existing software packages.Dissertation913 385 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, The Inside-Outside Duality in Inverse Scattering Theory(2016-05-20); ; ; In this thesis we investigate a connection between far field data that arises from time-harmonic scattering problems and interior eigenvalues of corresponding scattering objects. This connection has been used to develop the so-called ``inside-outside duality`` method, which can be used to detect the interior eigenvalues from far field data. In this method a particular focus lies on the behavior of certain eigenvalues of the far field operator, which characterizes the interior eigenvalues. This thesis is separated into two parts. In the first part, we consider acoustic, time-harmonic scattering from impenetrable and penetrable scattering objects. We start by considering acoustic scattering from impenetrable objects and subsequently outline the principle arguments for the derivation of the inside-outside duality. In this context we also show how to work with near field data instead of far field data. In the remainder of the first part, the arguments are then adapted to scattering from penetrable scattering objects that may contain cavities. For all scattering scenarios under investigation, numerical examples for the verification of the theoretical results are provided. In the second part of this thesis we consider elastic and electromagnetic scattering problems. In the case of elastic scattering, we assume an isotropic background medium in which either a rigid or a penetrable scattering object is embedded. For electromagnetic scattering, we consider penetrable objects that may contain cavities. The main challenge in this part lies in adapting the preceding arguments for the different scattering equations. Therefore we focus on theoretical results, which can potentially be used to detect interior eigenvalues from corresponding far field data.Dissertation507 485