Computational mathematics

The method for finding activity discontinues in positron emission tomography

I. P. Yarovenko<sup>ab

a</sup> Institute of Applied Mathematics FEB RAS, st. Radio, 7, 690041, Vladivostok, Russia
^b Far Eastern Federal University, st. Sukhanova, 8, 690950, Vladivostok, Russia

Abstract: This paper deals with the inverse problem of a positron emission tomography. It is assumed that the outgoing radiation density is only given, and the task is to find the surface of an activity source. The uniqueness of the solution is proved, and the corresponding solution algorithm is outlined. Some numerical results are presented in graphical form for reconstructing the boundaries of unknown activity sources.

Keywords: positron emission tomography, radiation transfer theory.

UDC: 517.958

MSC: 35Q60, 35R30

Received June 6, 2016, published August 24, 2016

DOI: 10.17377/semi.2016.13.054

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