Reflections are a common artifact in images taken through glass windows. Automatically removing the reflection artifacts after the picture is taken is an ill-posed problem. Attempts to solve this problem using optimization schemes therefore rely on various prior assumptions from the physical world. Instead of removing reflections from a single image, which has met with limited success so far, we propose a novel approach to suppress reflections. It is based on a Laplacian data fidelity term and an l0 gradient sparsity term imposed on the output. With experiments on artificial and real-world images we show that our reflection suppression method performs better than the state-of-the-art reflection removal techniques.