In the framework of the paper an improved method for image resolution enhancement is introduced. The enhancement is performed through another representation domain, where the image function is expressed with the help of polylinear functions on higher order singular value decomposition (HOSVD) basis. The paper gives a detailed description on how to determine the polylinear functions corresponding to an image and how to process them in order to obtain a higher resolution image. Furthermore, the proposed approach and the Fourier-based approach will be compared from the point of view of their effectiveness.