  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 work, we propose a
technique based on a novel optimisation problem. Firstly, we introduce a simple
user interaction scheme, which helps minimise information loss in
reflection-free regions. Secondly, we introduce an $H^2$ fidelity term, which
preserves fine detail while enforcing global colour similarity. We show that
this combination allows us to mitigate some major drawbacks of 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 methods
and compete with recent deep-learning approaches.
