There are several methods for improving the resolution of images. The usual approach is by sparsely representing patches in a low-resolution input image via a dictionary of an example low-resolution patches and then using the coefficients of this representation to generate the high-resolution output via an analogous high-resolution dictionary. However, most existing methods focus on luminance channel information only and neglect the colour channels. The present method achieves sparsity-based super resolution by considering multiple colour channels also along with luminance channel Information. Edge similarities among RGB colour bands are used as cross channel correlation constraints. A dictionary learning method specifically to learn colour dictionaries that encourage edge similarities is also used. The advantages of this method are demonstrated both visually and quantitatively using image quality metrics.