Wide-sense stationarity in generalized graph signal processing
We consider statistical graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. This general model encompasses various signals such as the traditional scalar-valued graph signal, multichannel graph signal, and disc...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/161585 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | We consider statistical graph signal processing (GSP) in a generalized
framework where each vertex of a graph is associated with an element from a
Hilbert space. This general model encompasses various signals such as the
traditional scalar-valued graph signal, multichannel graph signal, and
discrete- and continuous-time graph signals, allowing us to build a unified
theory of graph random processes. We introduce the notion of joint wide-sense
stationarity in this generalized GSP framework, which allows us to characterize
a graph random process as a combination of uncorrelated oscillation modes
across both the vertex and Hilbert space domains. We elucidate the relationship
between the notions of wide-sense stationarity in different domains, and derive
the Wiener filters for denoising and signal completion under this framework.
Numerical experiments on both real and synthetic datasets demonstrate the
utility of our generalized approach in achieving better estimation performance
compared to traditional GSP or the time-vertex framework. |
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