TY - GEN
T1 - On the Generalized Sampling Expansion (GSE) for Graph Signals
AU - Rajguru, Reeteswar
AU - Udayagiri, Balaji
AU - Budkuley, Amitalok J.
AU - Rini, Stefano
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85202807593&partnerID=8YFLogxK
U2 - 10.1109/ISIT57864.2024.10619682
DO - 10.1109/ISIT57864.2024.10619682
M3 - Conference contribution
AN - SCOPUS:85202807593
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2245
EP - 2250
BT - 2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2024 IEEE International Symposium on Information Theory, ISIT 2024
Y2 - 7 July 2024 through 12 July 2024
ER -