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A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces

Jin, Qinian; Lu, Xiliang

Description

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the Hilbert space structure of the underlying problems, we propose a fast iterative regularization method which reduces to the classical nonstationary iterated Tikhonov regularization when the penalty term is chosen to be the square of norm. Each iteration of the...[Show more]

dc.contributor.authorJin, Qinian
dc.contributor.authorLu, Xiliang
dc.date.accessioned2015-12-10T23:35:05Z
dc.date.available2015-12-10T23:35:05Z
dc.identifier.issn0266-5611
dc.identifier.urihttp://hdl.handle.net/1885/69702
dc.description.abstractIn this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the Hilbert space structure of the underlying problems, we propose a fast iterative regularization method which reduces to the classical nonstationary iterated Tikhonov regularization when the penalty term is chosen to be the square of norm. Each iteration of the method consists of two steps: the first step involves only the operator from the problem while the second step involves only the penalty term. This splitting character has the advantage of making the computation efficient. In case the data is corrupted by noise, a stopping rule is proposed to terminate the method and the corresponding regularization property is established. Finally, we test the performance of the method by reporting various numerical simulations, including the image deblurring, the determination of source term in Poisson equation, and the de-autoconvolution problem.
dc.publisherInstitute of Physics Publishing
dc.sourceInverse Problems
dc.titleA fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume30
dc.date.issued2014
local.identifier.absfor010303 - Optimisation
local.identifier.ariespublicationU3488905xPUB2097
local.type.statusPublished Version
local.contributor.affiliationJin, Qinian, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationLu, Xiliang, Wuhan University
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage045012
local.identifier.doi10.1088/0266-5611/30/4/045012
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2015-12-10T11:38:43Z
local.identifier.scopusID2-s2.0-84897451591
local.identifier.thomsonID000333849100012
CollectionsANU Research Publications

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