Kontak, Max and Michel, Volker (2019) The Regularized Weak Functional Matching Pursuit for linear inverse problems. Journal of Inverse and Ill-posed Problems, 27 (3), pp. 317-340. de Gruyter. doi: 10.1515/jiip-2018-0013. ISSN 0928-0219.
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Official URL: https://www.degruyter.com/view/j/jiip.2019.27.issue-3/jiip-2018-0013/jiip-2018-0013.xml
Abstract
In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the "weak" approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90% of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.
Item URL in elib: | https://elib.dlr.de/128196/ | |||||||||
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Document Type: | Article | |||||||||
Title: | The Regularized Weak Functional Matching Pursuit for linear inverse problems | |||||||||
Authors: |
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Date: | June 2019 | |||||||||
Journal or Publication Title: | Journal of Inverse and Ill-posed Problems | |||||||||
Refereed publication: | Yes | |||||||||
Open Access: | No | |||||||||
Gold Open Access: | No | |||||||||
In SCOPUS: | Yes | |||||||||
In ISI Web of Science: | Yes | |||||||||
Volume: | 27 | |||||||||
DOI: | 10.1515/jiip-2018-0013 | |||||||||
Page Range: | pp. 317-340 | |||||||||
Publisher: | de Gruyter | |||||||||
ISSN: | 0928-0219 | |||||||||
Status: | Published | |||||||||
Keywords: | Convergence rate, greedy algorithm, ill-posed problem, inverse problem, non-linear approximation, Tikhonov regularization | |||||||||
HGF - Research field: | Aeronautics, Space and Transport | |||||||||
HGF - Program: | Space | |||||||||
HGF - Program Themes: | Space System Technology | |||||||||
DLR - Research area: | Raumfahrt | |||||||||
DLR - Program: | R SY - Space System Technology | |||||||||
DLR - Research theme (Project): | R - Vorhaben SISTEC (old) | |||||||||
Location: | Köln-Porz | |||||||||
Institutes and Institutions: | Institut of Simulation and Software Technology > High Performance Computing | |||||||||
Deposited By: | Kontak, Max | |||||||||
Deposited On: | 30 Oct 2019 11:20 | |||||||||
Last Modified: | 30 Oct 2019 11:20 |
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