IEEE Open Journal of Signal Processing (Jan 2023)

Multi-Channel Sampling on Graphs and Its Relationship to Graph Filter Banks

  • Junya Hara,
  • Yuichi Tanaka

DOI
https://doi.org/10.1109/OJSP.2023.3249112
Journal volume & issue
Vol. 4
pp. 148 – 156

Abstract

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In this article, we consider multi-channel sampling (MCS) for graph signals. We generally encounter full-band graph signals beyond the bandlimited ones in many applications, such as piecewise constant/smooth graph signals and union of bandlimited graph signals. Full-band graph signals can be represented by a mixture of multiple signals conforming to different generation models. This requires the analysis of graph signals via multiple sampling systems, i.e., MCS, while existing approaches only consider single-channel sampling. We develop a MCS framework based on generalized sampling. We also present a sampling set selection (SSS) method for the proposed MCS so that the graph signal is best recovered. Furthermore, we reveal that existing graph filter banks can be viewed as a special case of the proposed MCS. In signal recovery experiments, the proposed method exhibits the effectiveness of recovery for full-band graph signals.

Keywords