Discrete Signal Processing on Graphs: Sampling Theory


We tend to propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We tend to show that excellent recovery is possible for graph signals bandlimited beneath the graph Fourier rework. The sampled signal coefficients type a brand new graph signal, whose corresponding graph structure preserves the first-order difference of the initial graph signal. For general graphs, an optimal sampling operator primarily based on experimentally designed sampling is proposed to ensure perfect recovery and robustness to noise; for graphs whose graph Fourier transforms are frames with maximal robustness to erasures along with for Erdős-Rényi graphs, random sampling leads to good recovery with high chance. We additional establish the affiliation to the sampling theory of finite discrete-time Signal Processing and previous work on signal recovery on graphs. To handle full-band graph signals, we have a tendency to propose a graph filter bank based mostly on sampling theory on graphs. Finally, we apply the proposed sampling theory to semi-supervised classification of online blogs and digit pictures, where we tend to achieve similar or higher performance with fewer labeled samples compared to previous work.

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