In this paper, we propose a new fast image interpolation method involving super-resolution effects. We use FREBAS transform to obtain multi-directional multi-resolution sub-images. By using the similarity of sub-images between different size images, sub-images beyond the Nyquist frequency is estimated using the FREBAS transformed images corresponding scaling parameter. Experiments showed that obtained images have much more sharpened structure than super resolution method based on dictionary learning. PSNR and SSIM are improved and calculation cost is very small compared to learning based method.