Despite the recent advances in smoke detection from video, detection of smoke from single images is still a challenging problem with both practical and theoretical implications. However, there is hardly any reported research on this topic in the literature. This paper addresses this problem by proposing a novel feature to detect smoke in a single image. An image formation model that expresses an image as a linear combination of smoke and non-smoke (background) components is derived based on the atmospheric scattering models. The separation of the smoke and non-smoke components is formulated as convex optimization that solves a sparse representation problem. Using the separated quasi-smoke and quasi-background components, the feature is constructed as a concatenation of the respective sparse coefficients. Extensive experiments were conducted and the results have shown that the proposed feature significantly outperforms the existing features for smoke detection.