On Uncertainty Principles for Lowband Graph Signals

In recent years, the research of graph signal processing has attracted extensive attention of scholars, especially graph uncertainty principle. The lower bound of uncertainty is closely related to time-frequency resolution, therefore it is of great application value to explore the minimum lower bound of uncertainty in time-frequency analysis, biological data processing and radar imaging. In this paper, we obtain two uncertainty principles of lowband graph signals, basing on matrix theory and operator norm theory. By using the extreme value property of quadratic matrix eigenvalue and the related definition of matrix norm, the basic sparse uncertainty principle and the sparse lower bound of graph uncertainty principle based on multiplicative uncertainty are compared, which shows the superiority of the latter in signal detection performance. Then, examples and numerical comparison results are provided to verify the previous theoretical analysis, showing that the graph uncertainty principle based on multiplicative uncertainty is closer to the time-frequency resolution than the basic sparse uncertainty principle. The application of uncertainty principle involving signal sparsity expansion in compressed sampling is also given.