Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-6040
Main Title: Wavelet methods for a weighted sparsity penalty for region of interest tomography
Author(s): Klann, Esther
Quinto, Eric Todd
Ramlau, Ronny
Type: Article
Language Code: en
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.
URI: http://depositonce.tu-berlin.de/handle/11303/6532
http://dx.doi.org/10.14279/depositonce-6040
Issue Date: 2015
Date Available: 27-Jul-2017
DDC Class: 530 Physik
004 Informatik
Subject(s): region of interest tomography
uniqueness
wavelets
sparsity
piecewise constant
Sponsor/Funder: FWF, T 529-N18, Mumford-Shah models for tomography II
NSF, 1311558, Tomography and Microlocal Analysis
FWF, W 1214, Doktoratskolleg "Computational Mathematics"
Usage rights: Terms of German Copyright Law
Journal Title: Inverse problems
Publisher: IOP Publishing
Publisher Place: Bristol [u.a.]
Volume: 31
Article Number: 025001
Publisher DOI: 10.1088/0266-5611/31/2/025001
EISSN: 1361-6420
ISSN: 0266-5611
Appears in Collections:Technische Universität Berlin » Fakultäten & Zentralinstitute » Fakultät 2 Mathematik und Naturwissenschaften » Institut für Mathematik » Fachgebiet Numerische Mathematik » Publications

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