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arXiv · 2211.02287

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

Junya Hara·Yuichi Tanaka
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Abstract

In this paper, we consider multi-channel sampling (MCS) for graph signals. We generally encounter full-band graph signals beyond the bandlimited one in many applications, such as piecewise constant/smooth 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.

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Junya Hara, Yuichi Tanaka. 2022-11-04. Multi-channel Sampling on Graphs and Its Relationship to Graph Filter Banks. https://arxiv.org/abs/2211.02287

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