S. Lasota, W. Niemiro and J. Koronacki

Positron Emission Tomography by Markov Chain Monte Carlo with Auxiliary Variables: A Basic Algorithm

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Abstract

In the report, an algorithm for positron emission tomography (PET) image reconstruction is proposed. The algorithm belongs to the family of Markov chain Monte Carlo methods with auxiliary variables. The well-known model of Vardi et al. (1985) is used for PET. The fact that an image consists of finitely many, in fact relatively few, gray-levels of uknown values is explicitly used to advantage: in the algorithm, the levels are represented by a fixed number of labels, so that at one step of the algorithm current approximation to the image is easily described by a configuration of finitely many labels and at another step real-valued intensities are assigned to each label. The algorithm decomposes naturally into the image restoration algorithm and the additional reconstruction (or generalized deconvolution) step. Simulation results are included which suggest that the method proposed is truly reliable and worth further study leading to practical implementation.

Key words: positron emission tomography; Swendsen-Wang algorithm; Markov chain Monte Carlo; inverse and ill-posed problems; intensity estimation