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The stochastic differential and integral equations describing the system ofparticles weakly interacting among themselves which are absorbed and scatteredby particles of a medium are considered. The time-dependent transport equationwith scattering is studied taking into account stochastic nature of parametersin nuclear imaging. Using dynamic attenuated Radon transform the solution oftransport equation may be derived taking into account of the scattering asperturbation. We analyze the influence of the random variables upon the imagereconstruction 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 causeessential distortions of image texture and degradation of the resolution atimage reconstruction in single-photon emission computerized tomography (SPECT)and less in X-ray computerized tomography (CT). The mechanism of thesedistortions is analyzed. The way for their elimination is shown for pointsources. We demonstrate that for the practical purposes it is enough to defineaveraged attenuation coefficient in investigated area when its difference fromtrue attenuation coefficient has certain stochastic properties. It is shownthat for positron emission tomography (PET) stochastic components in parametersof a transport model without the scattering can be taken into account of thecorrections of projections.

Stochastic Aspect of the Tomographic Reconstruction Problems in a Transport Model