Kazimierski, Kamil
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Kazimierski, Kamil
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Kazimierski, Kamil
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Item type:Publication, Regularization of the inverse medium problem : on nonstandard methods for sparse reconstruction(2014-12-19); ; ; In this thesis, we investigate nonstandard methods for the stable solution of the inverse medium problem. Particularly, we consider the linearization of the model of the scattering process given by the Born approximation and investigate regularization methods that are designed for sparse reconstruction. In numerical experiments we demonstrate that sparsity constraints contribute to meaningful reconstructions from synthetic and even measurement data. In our investigations, we consider both iterative and variational methods for the solution of the inverse problem. Starting from the Landweber iteration, we discuss existing variants of this approach and develop a novel sparsity-enforcing method which is based on the Bregman projection. Furthermore, we consider a variational regularization scheme. First, we develop a novel parameter choice rule based on the L-curve criterion designed for sparse reconstruction. We then propose to replace the variational problem by some smooth approximation and provide an exhaustive investigation regarding stability of this approach. The theoretical investigations of each of the methods proposed in this work are complemented by a numerical evaluation.doctoral thesis378 204 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, 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.doctoral thesis913 386