Removing reflection artefacts from a single image is a problem of both theoretical and practical interest, which still presents challenges because of the massively ill-posed nature of the problem. In this paper, we propose a technique based on a novel optimization problem. First, we introduce a simple user interaction scheme, which helps minimize information loss in the reflection-free regions. Second, we introduce an H 2 fidelity term, which preserves fine detail while enforcing the global color similarity. We show that this combination allows us to mitigate the shortcomings in structure and color preservation, which presents some of the most prominent drawbacks in the existing methods for reflection removal. We demonstrate, through numerical and visual experiments, that our method is able to outperform the state-of-the-art model-based methods and compete with recent deep-learning approaches.