Wavelet methods for a weighted sparsity penalty for region of interest tomography

dc.contributor.authorKlann, Esther
dc.contributor.authorQuinto, Eric Todd
dc.contributor.authorRamlau, Ronny
dc.date.accessioned2017-07-27T15:20:20Z
dc.date.available2017-07-27T15:20:20Z
dc.date.issued2015
dc.description.abstractWe consider region of interest (ROI) tomography of piecewise constant functions. Additionally, an algorithm is developed for ROI tomography of piecewise constant functions using a Haar wavelet basis. A weighted ℓp–penalty is used with weights that depend on the relative location of wavelets to the region of interest. We prove that the proposed method is a regularization method, i.e., that the regularized solutions converge to the exact piecewise constant solution if the noise tends to zero. Tests on phantoms demonstrate the effectiveness of the method.en
dc.description.sponsorshipFWF, T 529-N18, Mumford-Shah models for tomography IIen
dc.description.sponsorshipNSF, 1311558, Tomography and Microlocal Analysisen
dc.description.sponsorshipFWF, W 1214, Doktoratskolleg "Computational Mathematics"en
dc.identifier.eissn1361-6420
dc.identifier.issn0266-5611
dc.identifier.urihttp://depositonce.tu-berlin.de/handle/11303/6532
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-6040
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc530 Physiken
dc.subject.ddc004 Datenverarbeitung; Informatiken
dc.subject.otherregion of interest tomographyen
dc.subject.otheruniquenessen
dc.subject.otherwaveletsen
dc.subject.othersparsityen
dc.subject.otherpiecewise constanten
dc.titleWavelet methods for a weighted sparsity penalty for region of interest tomographyen
dc.typeArticleen
dc.type.versionacceptedVersionen
dcterms.bibliographicCitation.articlenumber025001en
dcterms.bibliographicCitation.doi10.1088/0266-5611/31/2/025001en
dcterms.bibliographicCitation.journaltitleInverse problemsen
dcterms.bibliographicCitation.originalpublishernameIOP Publishingen
dcterms.bibliographicCitation.originalpublisherplaceBristol [u.a.]en
dcterms.bibliographicCitation.volume31en
tub.accessrights.dnbdomainen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>FG Numerische Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Numerische Mathematikde
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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