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Citation link: http://nbn-resolving.de/urn:nbn:de:gbv:46-00107828-15
00107828-1.pdf
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Effective and Efficient Reconstruction Schemes for the Inverse Medium Problem in Scattering


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Other Titles: Effektive und effiziente Rekonstruktionsmethoden für inverse Streuprobleme in Medien
Authors: Bürgel, Florian  
Supervisor: Lechleiter, Armin
1. Expert: Kazimierski, Kamil S.
2. Expert: Hohage, Thorsten
Abstract: 
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.
Keywords: Inverse Scattering Problem, Parameter Identification, Helmholtz Equation, Denoising, Sparsity Regularization, Total Variation Regularization, Primal-Dual Algorithm, Factorization Method, MATLAB Toolbox
Issue Date: 19-Aug-2019
Type: Dissertation
URN: urn:nbn:de:gbv:46-00107828-15
Institution: Universität Bremen 
Faculty: FB3 Mathematik/Informatik 
Appears in Collections:Dissertationen

  

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