By means of numerical methods, the question is studied of applicability of the inhomogeneity indicator in positron emission tomography. The signal registered by the tomograph is described in terms of an imitation model using the Monte Carlo method. The possibility is demonstrated of the effective use of the inhomogeneity indicator for solving the problem under consideration. Some numerical results are presented in graphical form for reconstructing the boundaries of unknown activity sources.The foundation of positron emission tomography (PET) are based on the idea of registration of two oppositely directed gamma-quanta appearing as a result of annihilation of the positrons emitted by a special agent introduced into the patient's body. Under this approach, the functioning of the tomograph's detectors function, depending on one another. If two detectors simultaneously register a signal (i.e., the so-called coincidence happens) then it is assumed that the annihilation point is situated on the line joining the detectors. This line is called the line of response. The registration of a pair of photons allows us to proceed without the collimators in determining the direction of the gamma-quanta movement and is a specific filter which helps distinguishing exactly those trajectories of photons that carry the necessary information on the distribution of the activity source in the matter [1].The majority of scanners can function both in the slice-by-slice mode (when the axial collimation is created with the help of the special tungsten plates called the septa), and in the three-dimensional mode (when the septa are pulled in and the coincidences are registered between all possible pairs of detectors). The usage of collimation leads to diminishing the random components in the detected signal. At the same time, a three-dimensional PET system, allowing registering the coincidences between any rings of detectors, leads to an eight-fold increase of the number of registered coincidences in comparison with the slice-by-slice regime [2], which amplifies the sensitivity of the tomograph and allows faster accumulating the necessary volume of information. In connection with this, the considered research area is most promising [1]. However, increase of the total number of registered events leads inevitably to increase of the quantity of random events whose effect on the reconstruction quality is negative. For example, registration of the scattered photons results in distinguishing some false response lines. This circumstance, in turn, leads to the necessity of development of new information processing methods [1].The main body of research in this area is directed to the construction of various empirical formulas and methods to allow estimating the contribution of the scattered radiation into the signal registered by the detectors and distinguishing the nonscattered (ballistic) portion of radiation [3][4][5][6][7][8][9][10][11]. After that the tomography problem is reduced to a simple inversion of the Radon transform, and the theory in th...