Clustering based downsampling and reconstruction for band-limited graph signal

Abstract

Graphs are flexible data representation tools, suitable for modeling the geometric structure of topologically complicated domains which signals reside. Signal processing on graphs extends signal processing concepts and methodologies from classical signal processing theory to data indexed by general graphs. Band-limited graph signal can be reconstructed from sampled data on a sub-set of the vertices by exploiting its spatial correlation. The Laplacian matrix contains the important information of graph structure. In this paper, we propose a band-limited graph signal downsampling algorithm and its corresponding reconstruction strategy based on the Laplacian Eigenvector, using graph signal processing concepts and clustering strategy. The proposed downsampling algorithm can efficiently captures the critical downsampling vertex according to the cut-off frequency of the graph-spectral domain. Experiments are conducted to show the effectiveness of the proposed strategy.