The first part of the doctoral dissertation deals with the precise identification of overlapping stellar objects in astronomical images that can be approximated by 2D Gaussian profiles. A method for robust estimation of overlapped 2D Gaussian components was developed that outperforms existing methods and resolves overlap even beyond the resolution limit in certain cases. The second part of the doctoral dissertation deals with the parameter estimation of the multidimensional Gaussian profile. A fast method for estimating the Gaussian profile of an arbitrary dimension in the domain of the exponential function argument was proposed. For a given initial centroid position, the method provides an analytical solution for all other Gaussian profile parameters. The third part of the doctoral dissertation deals with the reconstruction of an unknown 2D distribution in low-dose 2D positron emission tomography (PET). In low-dose 2D PET, image reconstruction by using conventional methods does not resemble the original process due to an insufficient number of coincident events to describe the underlying process. As part of this research, a new method for data acquisition in low-dose PET was developed, where virtual response lines, i.e., coincident events, are artificially generated at the intersections of the original response lines, thereby artificially increasing the input dataset. The method is based on the relationship between spatial statistical properties of intersections of response lines and the process samples, which were derived and analyzed in detail within this dissertation.