Diagnostics is one of the most rapidly developing areas of medicine. SPECT (Single Photon Emission Computed Tomography) is one of the modernest of nuclear imaging methods, which represents a progress in quality of diagnostic procedures. It is primarily used for diagnosing diseases of the heart, brain and bones, and it is of great importance in diagnosing malignancies. The method is quite sensitive, and due to the good spatial resolution, smaller lesions can also be identified. With the use of SPECT, diseases can be diagnosed faster and more accurately, and the progression of disease and effects of therapeutic interventions can also be followed. The use of this imaging technique enables us to construct images at the molecular level, that is we can detect biochemical changes due to pathological processes, when they have not even triggered symptoms. The aim of thesis planning was to improve the running time of the image reconstruction algorithms for which the distance dependent point spread function (PSF) had been used. We wanted to replace the PSF model since the running time of the PSF codes is highly dependent on the variance of the Gaussian kernel. The higher it is, i.e. the wider the Gaussian kernel is, the longer it takes to run the reconstruction. First, the point spread function was approached with a diffusion partial difference equation, then it was examined how much it differs from the earlier results of the Gaussian spread. Another method, the so called slice-to-slice blurring method, was also used for the acceleration of the running time. Basically, the picture is blurred slice by slice, which enables us to use Gaussian functions with lower variance. The result of this method was also compared to that of the PSF model.