Wavelet methods for a weighted sparsity penalty for region of interest tomography
| dc.contributor.author | Klann, Esther | |
| dc.contributor.author | Quinto, Eric Todd | |
| dc.contributor.author | Ramlau, Ronny | |
| dc.date.accessioned | 2017-07-27T15:20:20Z | |
| dc.date.available | 2017-07-27T15:20:20Z | |
| dc.date.issued | 2015 | |
| dc.description.abstract | We 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.sponsorship | FWF, T 529-N18, Mumford-Shah models for tomography II | en |
| dc.description.sponsorship | NSF, 1311558, Tomography and Microlocal Analysis | en |
| dc.description.sponsorship | FWF, W 1214, Doktoratskolleg "Computational Mathematics" | en |
| dc.identifier.eissn | 1361-6420 | |
| dc.identifier.issn | 0266-5611 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/6532 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-6040 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 530 Physik | en |
| dc.subject.ddc | 004 Datenverarbeitung; Informatik | en |
| dc.subject.other | region of interest tomography | en |
| dc.subject.other | uniqueness | en |
| dc.subject.other | wavelets | en |
| dc.subject.other | sparsity | en |
| dc.subject.other | piecewise constant | en |
| dc.title | Wavelet methods for a weighted sparsity penalty for region of interest tomography | en |
| dc.type | Article | en |
| dc.type.version | acceptedVersion | en |
| dcterms.bibliographicCitation.articlenumber | 025001 | en |
| dcterms.bibliographicCitation.doi | 10.1088/0266-5611/31/2/025001 | en |
| dcterms.bibliographicCitation.journaltitle | Inverse problems | en |
| dcterms.bibliographicCitation.originalpublishername | IOP Publishing | en |
| dcterms.bibliographicCitation.originalpublisherplace | Bristol [u.a.] | en |
| dcterms.bibliographicCitation.volume | 31 | en |
| tub.accessrights.dnb | domain | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Numerische Mathematik | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |