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Main Title: A Mumford–Shah-type approach to simultaneous reconstruction and segmentation for emission tomography problems with Poisson statistics
Author(s): Klann, Esther
Ramlau, Ronny
Sun, Peng
Type: Article
Language Code: en
Abstract: We propose a variational model to simultaneous reconstruction and segmentation in emission tomography. As in the original Mumford–Shah model [27] we use the contour length as penalty term to preserve edge information whereas a different data fidelity term is used to measure the information discrimination between the computed tomography data of the reconstructed object and the observed (or simulated) data. As data fidelity term we use the Kullback–Leibler divergence which originates from the Poisson distribution present in emission tomography. In this paper we focus on piecewise constant reconstructions which is a reasonable assumption in medical imaging. The segmenting contour as well as the corresponding reconstructions are found as minimizers of a Mumford–Shah-type functional over the space of piecewise constant functions. The numerical scheme is implemented by evolving the level-set surface according to the shape derivative of the functional. The method is validated for simulated data with different levels of noise.
Issue Date: 2017
Date Available: 27-Jul-2017
DDC Class: 510 Mathematik
Subject(s): ill-posed problem
regularization method
level-set method
Poisson statistics
Sponsor/Funder: EC/FP7/600209/EU/International Post-Doc Initiative of the Technische Universität Berlin/IPODI
FWF, T 529-N18, Mumford-Shah models for tomography II
FWF, W 1214, Doktoratskolleg "Computational Mathematics"
Journal Title: Journal of inverse and ill-posed problems
Publisher: De Gruyter
Publisher Place: Berlin
Publisher DOI: 10.1515/jiip-2016-0077
EISSN: 1569-3945
ISSN: 0928-0219
Appears in Collections:FG Numerische Mathematik » Publications

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