An Efficient Approach for Image Resolution Enhancement Using Multi Step Magnification Method The lowresolution image is viewed as down sampled version of a highresolution image, whose patches are assumed to have a sparse representation with respect to an overcomplete dictionary of prototype signalatoms. The principle of compressed sensing ensures that under mild conditions, the sparse representation can be correctly recovered from the down sampled signal. We will demonstrate the effectiveness of sparsity as a prior for regularizing the otherwise illposed superresolution problem. We further show that a small set of randomly chosen raw patches from training images of similar statistical nature to the input image generally serve as a good dictionary, in the sense that the computed representation is sparse and the recovered high resolution image is competitive or even superior in quality to images produced by other SR methods.

Image superresolution with sparse representation prior on primitive patches We focus on the problem of single image superresolution in this paper. Given a lowresolution image, we seek to synthesize its underlying highresolution details using a learning based method. Inspired by recent progress in compressive sensing, we use sparse representation prior to regularize this illposed problem. On the other hand, with natural image statistics taken into consideration, we enforce the prior only on those image patches associated with image primitives rather than on arbitrary ones. Specifically, each patch from primitive layer of the lowresolution image, which can be viewed as a lowdimensional projection of a highresolution primitive patch, is conjectured to have a sparse representation concerning an overcomplete dictionary. Under mild conditions, the sparse representation can be correctly restored from the lowdimensional projection according to the theory of compressive sensing. We also construct a dictionary using image primitive patches which works well on generic input images. Experiment results show the efficiency of our method by outperforming other learningbased methods both subjectively and objectively.