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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.
Issue Date: 2015
Date Available: 27-Jul-2017
DDC Class: 530 Physik
004 Datenverarbeitung; Informatik
Subject(s): region of interest tomography
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"
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:FG Numerische Mathematik » Publications

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