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The Regularized Weak Functional Matching Pursuit for linear inverse problems

Kontak, Max and Michel, Volker (2018) The Regularized Weak Functional Matching Pursuit for linear inverse problems. Journal of Inverse and Ill-posed Problems. de Gruyter. DOI: 10.1515/jiip-2018-0013 ISSN 0928-0219 (In Press)

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Official URL: https://www.degruyter.com/view/j/jiip.ahead-of-print/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/122987/
Document Type:Article
Additional Information:The final publication is available at www.degruyter.com.
Title:The Regularized Weak Functional Matching Pursuit for linear inverse problems
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Kontak, MaxMax.Kontak (at) DLR.dehttps://orcid.org/0000-0003-3738-7483
Michel, VolkerUniversität Siegenhttps://orcid.org/0000-0002-2551-0491
Date:16 October 2018
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
DOI :10.1515/jiip-2018-0013
Publisher:de Gruyter
ISSN:0928-0219
Status:In Press
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 Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Technik für Raumfahrtsysteme
DLR - Research theme (Project):R - Vorhaben SISTEC
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology > High Performance Computing
Deposited By: Kontak, Max
Deposited On:26 Nov 2018 14:29
Last Modified:26 Nov 2018 14:29

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