Sparsity constrained single image super-resolution has been of much recent interest. A typical approach involves sparsely representing patches in a low-resolution (LR) input image via a dictionary of example LR patches, and then use the coefficients of this representation to generate the high-resolution (HR) output via an analogous HR dictionary. However, most existing sparse representation methods for super resolution only use luminance channel information and do not use any information from other color channels. In this work, we extend sparsity based super-resolution to multiple color channels. Edge similarities amongst color bands are exploited as cross channel correlation constraints. These additional constraints lead to a new optimization problem which is not easily solvable; however, a tractable solution is proposed to solve it efficiently. Experimental results shows the merits of our proposed method both visually and quantitatively.