A new iterative approach for the spectral extrapolation of an image is introduced. In the space domain it is only assumed that the image is non-negative and in the frequency domain it is assumed that its low frequency components are known. A modified version of the method of projections onto convex sets with relaxed parameters is implemented. It is shown that the proposed iterative method is nonexpansive and in some cases it is contractive and given the same constraints, it converges faster than Gerchberg iterative superresolution algorithm and gives a better result. It is also shown that in the cases when the algorithm becomes contractive it performs better in the presence of small amounts of noise in the low frequency components.