Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-6039
Main Title: Regularization properties of Mumford–Shah-type functionals with perimeter and norm constraints for linear ill-posed problems
Author(s): Klann, Esther
Ramlau, Ronny
Type: Article
Language Code: en
Abstract: In this paper we consider the simultaneous reconstruction and segmentation of a function f from measurements g = Kf, where K is a linear operator. Assuming that the inversion of K is illposed, regularization methods have to be used for the inversion process in case of inexact data. We propose using a Mumford–Shah-type functional for the stabilization of the inversion. Restricting our analysis to the recovery of piecewise constant functions, we investigate the existence of minimizers, their stability, and the regularization properties of our approach. Finally, we present a numerical example from single photon emission computed tomography (SPECT).
URI: http://depositonce.tu-berlin.de/handle/11303/6531
http://dx.doi.org/10.14279/depositonce-6039
Issue Date: 2013
Date Available: 27-Jul-2017
DDC Class: DDC::500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
Subject(s): regularization
ill-posed problems
Mumford–Shah
SPECT
Sponsor/Funder: FWF, T 529-N18, Mumford-Shah models for tomography II
Usage rights: Terms of German Copyright Law
Journal Title: SIAM journal on imaging sciences
Publisher: Society for Industrial and Applied Mathematics
Publisher Place: Philadelphia, Pa.
Volume: 6
Issue: 1
Publisher DOI: 10.1137/110858422
Page Start: 413
Page End: 436
EISSN: 1936-4954
Appears in Collections:Technische Universität Berlin » Fakultäten & Zentralinstitute » Fakultät 2 Mathematik und Naturwissenschaften » Institut für Mathematik » Fachgebiet Numerische Mathematik » Publications

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