Local-Set-Based Graph Signal Reconstruction

Signal processing on graph is attracting more and more attention. For a graph signal in the low-frequency space, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the smoothness of graph signal. In this paper, two local-set-based iterative methods are proposed to reconstruct bandlimited graph signal from sampled data. In each iteration, one of the proposed methods reweights the sampled residual for dierent vertices based on a measure corresponding to their local sets, while the other propagates the sampled residue bandlimitedly in their respective local set. These algorithms are built on frame theory and a introduced concept of local sets, based on which several frames and contraction operators are proposed. We then prove the reconstruction methods converge to the original signal under certain conditions and demonstrate the new methods lead to a signicantly faster convergence compared with the baseline method. Furthermore, the correspondence between graph signal sampling and time-domain irregular sampling is analyzed comprehensively, which may be helpful to future works on graph signals. Computer simulations are conducted. The experiment results demonstrate the eectiveness of the reconstruction methods in various sampling geometries, imprecise priori knowledge of cuto frequency, and noisy