Recently plenoptic cameras have gained much attention, as they capture the 4D light field of a scene which is useful for numerous computer vision and graphics applications. Similar to traditional digital cameras, plenoptic cameras use a color filter array placed onto the image sensor so that each pixel only samples one of three primary color values. A color demosaicing algorithm is then used to generate a full-color plenoptic image, which often introduces color aliasing artifacts. In this paper, we propose a dictionary learning based demosaicing algorithm that recovers a full-color light field from a captured plenoptic image using sparse optimization. Traditional methods consider only spatial correlations between neighboring pixels on a captured plenoptic image. Our method takes advantage of both spatial and angular correlations inherent in naturally occurring light fields. We demonstrate that our method outperforms traditional color demosaicing methods by performing experiments on a wide variety of scenes.