Local splines and it’s cubic polynomial splines, which are used traditionally, are used in solving many image processing problems. In this paper, we consider the use of local quadratic polynomial and trigonometric splines of the third order of approximation, as well as polynomial splines of the fifth order of approximation for image processing. The paper proposes an algorithm to increase the image (or its part) without loss of quality using local polynomial splines of the third and fifth order of approximation and trigonometric splines of the third order of approximation. This paper also developed an algorithm for compressing and restoring images using the considered splines. The theoretical background and results of numerical experiments are presented.