Single Image Super-Resolution (SISR) through sparse representation has received much attention in the past decade due to significant development in sparse coding algorithms. However, recovering high-frequency textures is a major bottleneck of existing SISR algorithms. Considering this, dictionary learning approaches are to be utilized to extract high-frequency textures which improve SISR performance significantly. In this paper, we have proposed the SISR algorithm through sparse representation which involves learning of Low Resolution (LR) and High Resolution (HR) dictionaries simultaneously from the training set. The idea of training coupled dictionaries preserves correlation between HR and LR patches to enhance the Super-resolved image. To demonstrate the effectiveness of the proposed algorithm, a visual comparison is made with popular SISR algorithms and also quantified through quality metrics. The proposed algorithm outperforms compared to existing SISR algorithms qualitatively and quantitatively as shown in experimental results. Furthermore, the performance of our algorithm is remarkable for a smaller training set which involves lesser computational complexity. Therefore, the proposed approach is proven to be superior based upon visual comparisons and quality metrics and have noticeable results at reduced computational complexity.