Aliasing artifacts in images are visually very disturbing. Therefore, most imaging devices apply a low-pass filter before sampling. This removes all aliasing from the image, but it also creates a blurred image. Actually, all the image information above half the sampling frequency is removed. In this paper, we present a new method for the reconstruction of a high resolution image from a set of highly undersampled and thus aliased images. We use the information in the entire frequency spectrum, including the aliased part, to create a sharp, high resolution image. The unknown relative shifts between the images are computed using a subspace projection approach. We show that the projection can be decomposed into multiple projections onto smaller subspaces. This allows for a considerable reduction of the overall computational complexity of the algorithm. A high resolution image can then be reconstructed from the registered low resolution images. Simulation results show the validity of our algorithm.