An Uncertainty Principle for Lowband Graph Signals

In this article, we introduce a novel lower bound on the support size of lowband graph signals. This result allows the deduction of an optimality criterion for the lowband and sparse decomposition of any graph signal, establishing the uniqueness of well behaving solutions. A comparison of the new bound with previously introduced results is performed, showing the improvements brought by the present work. An illustration on a practical denoising usecase on a real graph is also provided.