Many effective approaches designed to solve ill-posed and ill-conditioned problem had deficiencies to fulfill the needs of point spread function (PSF), which is hard to get into the practical situation all the time. So this project introduces a method called as Sparse signal representation for a single-image Super Resolution. The research on image Statistics gives a forward step to represent the image patches in a better way, as a sparse linear combination of elements, which are chosen from complete dictionary. From the coefficients of the sparse representation are utilized to construct the high-resolution output image. Here it trains two dictionaries jointly for the low-and high-resolution image patch, which produces two individual dictionary and it shows that the sparse representations for low- and high-resolution is same. To produce a high resolution image patch, the sparse representation can put together two trained dictionaries of the low- and the high-resolution image patch. A large amount of image patch pair are sampled here, by decreasing the computational cost significantly.