This article is cited in 1 paper

A formula for the gradient of the output signal in positron emission tomography

I. P. Yarovenko<sup>ab

a</sup> Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok
^b Far Eastern Federal University, Vladivostok

Abstract: The work is devoted to the study of qualitative properties for the mathematical model of positron emission tomography. The model is the integral transform of unknown function describing the distribution of activity sources. We propose a formula for the gradient of the output signal. We give conditions under which the gradient of the output signal will have a singularity.

Key words: radiation transfer theory, positron emission tomography.

UDC: 517.958

MSC: Primary 35Q60; Secondary 35R30

Received: 04.09.2014

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