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International Journal of Biomedical Imaging
Volume 2007 (2007), Article ID 26950, 15 pages
Research Article

Level Set Method for Positron Emission Tomography

1Department of Mathematics, University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, USA
2Center for Integrated Petroleum Research, University of Bergen, CIPR room 4103, All├ęgaten 41, Bergen 5007, Norway
3Department of Scientific Computing, Simula Research Laboratory AS, Lysaker 1325, Norway
4Department of Mathematics and System Sciences, Henan University, Kaifeng 475001, China
5Department of Mathematics, University of Bergen, Johannes Brunsgate 12, Bergen 5009, Norway

Received 26 December 2006; Accepted 6 May 2007

Academic Editor: Hongkai Zhao

Copyright © 2007 Tony F. Chan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In positron emission tomography (PET), a radioactive compound is injected into the body to promote a tissue-dependent emission rate. Expectation maximization (EM) reconstruction algorithms are iterative techniques which estimate the concentration coefficients that provide the best fitted solution, for example, a maximum likelihood estimate. In this paper, we combine the EM algorithm with a level set approach. The level set method is used to capture the coarse scale information and the discontinuities of the concentration coefficients. An intrinsic advantage of the level set formulation is that anatomical information can be efficiently incorporated and used in an easy and natural way. We utilize a multiple level set formulation to represent the geometry of the objects in the scene. The proposed algorithm can be applied to any PET configuration, without major modifications.