Discrete Signal Processing on Graphs: Sampling Theory

We 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 show that perfect recovery is possible for graph signals bandlimited under the graph Fourier transform. The sampled signal coefficients form a new graph signal, whose corresponding graph structure preserves the first-order difference of the original graph signal. For general graphs, an optimal sampling operator based on experimentally designed sampling is proposed to guarantee perfect recovery and robustness to noise; for graphs whose graph Fourier transforms are frames with maximal robustness to erasures as well as for Erdős-Rényi graphs,…

• NS
  National Science Foundation

  Awards: 1421919, 1130616
• UD
  U.S. Department of Transportation

  Award: DTRT12-GUTC11