  The stochastic differential and integral equations describing the system of
particles weakly interacting among themselves which are absorbed and scattered
by particles of a medium are considered. The time-dependent transport equation
with scattering is studied taking into account stochastic nature of parameters
in nuclear imaging. Using dynamic attenuated Radon transform the solution of
transport equation may be derived taking into account of the scattering as
perturbation. We analyze the influence of the random variables upon the image
reconstruction both generally and in more details for the case of point source.
It is shown by the example of the method of the filtered back projection (FBP)
that unaccounted small fluctuations of attenuation coefficient can cause
essential distortions of image texture and degradation of the resolution at
image reconstruction in single-photon emission computerized tomography (SPECT)
and less in X-ray computerized tomography (CT). The mechanism of these
distortions is analyzed. The way for their elimination is shown for point
sources. We demonstrate that for the practical purposes it is enough to define
averaged attenuation coefficient in investigated area when its difference from
true attenuation coefficient has certain stochastic properties. It is shown
that for positron emission tomography (PET) stochastic components in parameters
of a transport model without the scattering can be taken into account of the
corrections of projections.
