Abstarct: Abstract In recent years, the demand for facial recognition to identify individuals from video surveillance cameras has increased rapidly. As surveillance cameras are usually positioned far from the subject's face, the resolution of facial images captured by the cameras is very low, which makes face recognition challenging. To address the above challenge, various super resolution methods are proposed. Super resolution methods are divided into two categories: single image and multi image. In the first category, a high resolution image is reconstructed from a single low resolution image, while in the second category, a set of low resolution images of the scene is used to construct a high resolution image. In this research, we focus on single image super resolution of faces. To achieve super resolution in this thesis, three ideas are proposed. In the first idea, a heuristic method baxsed on Fourier transform is presented. For this purpose, the magnitude and phase of the Fourier transform are initially used separately to obtain an initial estimate of the high resolution image. Then, with the help of a backprojection algorithm, details are gradually added to the high resolution image. In the second idea, considering the higher capability of the fractional Fourier transform compared to the conventional Fourier transform, we use the fractional Fourier transform for super resolution. To select the fractional parameter, we use the particle swarm optimization algorithm. Considering that the blur in different parts of real scenes is not uniform, in the third idea, the low resolution image is segmented baxsed on the dimensions of the desired window. Then, the segments are clustered baxsed on their amount of blur, and a candidate segment is selected from each cluster, and baxsed on the second idea, the optimal fractional Fourier parameter is obtained for each cluster. The optimal fractional parameter of each cluster is applied to all segments related to its own cluster, and the super resolution operation is applied to all segments in this way. The quality of this method is higher than the previous methods, but the disadvantage that exists in it is the creation of boundary lines, which is caused by the difference in the optimal value of the fractional parameter of two adjacent sections. To remove these boundary lines, weighted averaging is used. In this way, to remove the boundaries, an optimal fractional parameter must be selected from among all the optimal parameters of the sections. For this purpose, the optimal parameter of the clusters is calculated baxsed on the number of sections of each cluster, and in this way, a candidate optimal fractional parameter is obtained. Then, by applying the selected optimal parameter in the second idea, the super resolution image is created from the low resolution image. Among the advantages of the proposed algorithms, we can mention their speed, simplicity, accuracy and performance quality according to the criteria obtained.