Total variation regularization in measurement and image space for PET reconstruction

Handle URI:
http://hdl.handle.net/10754/600042
Title:
Total variation regularization in measurement and image space for PET reconstruction
Authors:
Burger, M; Müller, J; Papoutsellis, E; Schönlieb, C B
Abstract:
© 2014 IOP Publishing Ltd. The aim of this paper is to test and analyse a novel technique for image reconstruction in positron emission tomography, which is based on (total variation) regularization on both the image space and the projection space. We formulate our variational problem considering both total variation penalty terms on the image and on an idealized sinogram to be reconstructed from a given Poisson distributed noisy sinogram. We prove existence, uniqueness and stability results for the proposed model and provide some analytical insight into the structures favoured by joint regularization. For the numerical solution of the corresponding discretized problem we employ the split Bregman algorithm and extensively test the approach in comparison to standard total variation regularization on the image. The numerical results show that an additional penalty on the sinogram performs better on reconstructing images with thin structures.
Citation:
Burger M, Müller J, Papoutsellis E, Schönlieb CB (2014) Total variation regularization in measurement and image space for PET reconstruction. Inverse Problems 30: 105003. Available: http://dx.doi.org/10.1088/0266-5611/30/10/105003.
Publisher:
IOP Publishing
Journal:
Inverse Problems
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
18-Sep-2014
DOI:
10.1088/0266-5611/30/10/105003
Type:
Article
ISSN:
0266-5611; 1361-6420
Sponsors:
This work has been financially supported by the King Abdullah University of Science and Technology (KAUST) Award No. KUK-I1-007-43, the EPSRC first grant EP/J009539/1, the Royal Society International Exchange Award Nr. IE110314, and the German Science Foundation (DFG) through the Collaborative Research Centre SFB 656 subproject B2 and Cells-in-Motion Cluster of Excellence (EXC 1003 CiM), University of Munster.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBurger, Men
dc.contributor.authorMüller, Jen
dc.contributor.authorPapoutsellis, Een
dc.contributor.authorSchönlieb, C Ben
dc.date.accessioned2016-02-28T06:34:54Zen
dc.date.available2016-02-28T06:34:54Zen
dc.date.issued2014-09-18en
dc.identifier.citationBurger M, Müller J, Papoutsellis E, Schönlieb CB (2014) Total variation regularization in measurement and image space for PET reconstruction. Inverse Problems 30: 105003. Available: http://dx.doi.org/10.1088/0266-5611/30/10/105003.en
dc.identifier.issn0266-5611en
dc.identifier.issn1361-6420en
dc.identifier.doi10.1088/0266-5611/30/10/105003en
dc.identifier.urihttp://hdl.handle.net/10754/600042en
dc.description.abstract© 2014 IOP Publishing Ltd. The aim of this paper is to test and analyse a novel technique for image reconstruction in positron emission tomography, which is based on (total variation) regularization on both the image space and the projection space. We formulate our variational problem considering both total variation penalty terms on the image and on an idealized sinogram to be reconstructed from a given Poisson distributed noisy sinogram. We prove existence, uniqueness and stability results for the proposed model and provide some analytical insight into the structures favoured by joint regularization. For the numerical solution of the corresponding discretized problem we employ the split Bregman algorithm and extensively test the approach in comparison to standard total variation regularization on the image. The numerical results show that an additional penalty on the sinogram performs better on reconstructing images with thin structures.en
dc.description.sponsorshipThis work has been financially supported by the King Abdullah University of Science and Technology (KAUST) Award No. KUK-I1-007-43, the EPSRC first grant EP/J009539/1, the Royal Society International Exchange Award Nr. IE110314, and the German Science Foundation (DFG) through the Collaborative Research Centre SFB 656 subproject B2 and Cells-in-Motion Cluster of Excellence (EXC 1003 CiM), University of Munster.en
dc.publisherIOP Publishingen
dc.subjectpositron emission tomographyen
dc.subjecttotal variationen
dc.subjectvariational regularizationen
dc.titleTotal variation regularization in measurement and image space for PET reconstructionen
dc.typeArticleen
dc.identifier.journalInverse Problemsen
dc.contributor.institutionWestfalische Wilhelms-Universitat Munster, Munster, Germanyen
dc.contributor.institutionUniversitatsklinikum Munster, Munster, Germanyen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-I1-007-43en
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