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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/161585 |
| _version_ | 1826115121918771200 |
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| author | Jian, Xingchao Tay, Wee Peng |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Jian, Xingchao Tay, Wee Peng |
| author_sort | Jian, Xingchao |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T03:50:22Z |
| format | Journal Article |
| id | ntu-10356/161585 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:50:22Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1615852022-09-12T02:25:25Z Wide-sense stationarity in generalized graph signal processing Jian, Xingchao Tay, Wee Peng School of Electrical and Electronic Engineering Centre for Infocomm Technology (INFINITUS) Engineering::Electrical and electronic engineering Graph Signal Processing Hilbert Space Wide-Sense Stationarity Power Spectral Density 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. Ministry of Education (MOE) Submitted/Accepted version This work was supported by the Singapore Ministry of Education Academic Research Fund Tier 2 under Grant MOE-T2EP20220-0002. 2022-09-12T02:25:24Z 2022-09-12T02:25:24Z 2022 Journal Article Jian, X. & Tay, W. P. (2022). Wide-sense stationarity in generalized graph signal processing. IEEE Transactions On Signal Processing, 70, 3414-3428. https://dx.doi.org/10.1109/TSP.2022.3184455 1053-587X https://hdl.handle.net/10356/161585 10.1109/TSP.2022.3184455 2-s2.0-85133798060 70 3414 3428 en MOE-T2EP20220-0002 IEEE Transactions on Signal Processing © 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: https://doi.org/10.1109/TSP.2022.3184455. application/pdf application/pdf |
| spellingShingle | Engineering::Electrical and electronic engineering Graph Signal Processing Hilbert Space Wide-Sense Stationarity Power Spectral Density Jian, Xingchao Tay, Wee Peng Wide-sense stationarity in generalized graph signal processing |
| title | Wide-sense stationarity in generalized graph signal processing |
| title_full | Wide-sense stationarity in generalized graph signal processing |
| title_fullStr | Wide-sense stationarity in generalized graph signal processing |
| title_full_unstemmed | Wide-sense stationarity in generalized graph signal processing |
| title_short | Wide-sense stationarity in generalized graph signal processing |
| title_sort | wide sense stationarity in generalized graph signal processing |
| topic | Engineering::Electrical and electronic engineering Graph Signal Processing Hilbert Space Wide-Sense Stationarity Power Spectral Density |
| url | https://hdl.handle.net/10356/161585 |
| work_keys_str_mv | AT jianxingchao widesensestationarityingeneralizedgraphsignalprocessing AT tayweepeng widesensestationarityingeneralizedgraphsignalprocessing |