On the Generalized Sampling Expansion (GSE) for Graph Signals

Reeteswar Rajguru, Balaji Udayagiri, Amitalok J. Budkuley, Stefano Rini

研究成果: Conference contribution同行評審

摘要

In this work, we study the problem of distributed sampling and interpolation for perfect reconstruction of graph signals. In particular, we explore and present a generalization of Papoulis' classic generalized sampling expansion (GSE) to graph signals. We consider a single-time instance of a graph signal from a space of bandlimited graph signals, appropriately defined via the graph Fourier transform associated to the graph. For such bandlimited graph signals, we first identify a sufficient condition for perfect reconstruction via distributed sampler/interpolator pairs, in the spirit of the Shannon-Nyquist criterion. When this perfect reconstruction criteria is satisfied by the individual sampler rates, we then propose a distributed sampler/interpolator architecture which is shown to be achievable for the underlying bandlimited space. The results represent a unique generalization of Papoulis' generalized sampling expansion (GSE) paradigm to graph signals. Interestingly, our results show that such achievable schemes-comprising several pairs of individual sampler/interpolator pairs-are such that every component sampler can be essentially perceived as a concatenation of a pre-sampling filtering operation followed by binary vertex-sampling. The corresponding interpolator is then obtained as a linear transformation which is completely dependent on the vertex-sampling operation but is independent of the pre-sampling filter.

原文English
主出版物標題2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
發行者Institute of Electrical and Electronics Engineers Inc.
頁面2245-2250
頁數6
ISBN(電子)9798350382846
DOIs
出版狀態Published - 2024
事件2024 IEEE International Symposium on Information Theory, ISIT 2024 - Athens, 希臘
持續時間: 7 7月 202412 7月 2024

出版系列

名字IEEE International Symposium on Information Theory - Proceedings
ISSN(列印)2157-8095

Conference

Conference2024 IEEE International Symposium on Information Theory, ISIT 2024
國家/地區希臘
城市Athens
期間7/07/2412/07/24

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