Generalized Graph Spectral Sampling with Stochastic Priors

Hara, Junya; Tanaka, Yuichi; Eldar, Yonina C.

doi:10.1109/icassp40776.2020.9053720

Cited by 9 publications

(6 citation statements)

References 23 publications

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“…Investigating GSP systems beyond the bandlimited assumption will be beneficial for many practical applications since real data are often not bandlimited. Such examples include generalized graph sampling [22] and PGS sampling [7], [8], [72].…”

Section: Closing Remarksmentioning

confidence: 99%

Sampling Signals on Graphs: From Theory to Applications

Tanaka,

Eldar,

Ortega

et al. 2020

Preprint

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The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph signal processing (GSP), sampling on graphs has various promising applications. In this article, we review current progress on sampling over graphs focusing on theory and potential applications. Most methodologies used in graph signal sampling are designed to parallel those used in sampling for standard signals, however, sampling theory for graph signals significantly differs from that for Shannon-Nyquist and shift invariant signals. This is due in part to the fact that the definitions of several important properties, such as shift invariance and bandlimitedness, are different in GSP systems. Throughout, we discuss similarities and differences between standard and graph sampling and highlight open problems and challenges.

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Section: Closing Remarksmentioning

confidence: 99%

Sampling Signals on Graphs: From Theory to Applications

Tanaka,

Eldar,

Ortega

et al. 2020

Preprint

Self Cite

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“…For clarity, the classical definition of WSS is detailed in Appendix A. 1 M is assumed to be a divisor of N for simplicity.…”

Section: Graph Wide Sense Stationaritymentioning

confidence: 99%

“…There are many promising applications of graph signal sampling, such as sensor placement [27], filter bank designs [38]- [41], traffic monitoring [42], and semi-supervised learning [43], [44]. Most works focus on building parallels of Preliminary results of this work was presented in [1]. Junya Hara and Yuichi Tanaka are supported in part by JST PRESTO (JPMJPR1935) and JSPS KAKENHI (20H02145, 23H01415, 22J22176).…”

Section: Introductionmentioning

confidence: 99%

Graph Signal Sampling Under Stochastic Priors

Hara

Tanaka

Eldar

2023

IEEE Trans. Signal Process.

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We propose a generalized sampling framework for stochastic graph signals. Stochastic graph signals are characterized by graph wide sense stationarity (GWSS) which is an extension of wide sense stationarity (WSS) for standard timedomain signals. In this paper, graph signals are assumed to satisfy the GWSS conditions and we study their sampling as well as recovery procedures. In generalized sampling, a correction filter is inserted between the sampling and reconstruction operators to compensate for non-ideal measurements. We propose a design method for the correction filters to reduce the mean-squared error (MSE) between the original and reconstructed graph signals. We derive the correction filters for two cases: The reconstruction filter is arbitrarily chosen or predefined. The proposed framework allows for arbitrary sampling methods, i.e., sampling in the vertex or graph frequency domain. We show that the graph spectral response of the resulting correction filter parallels that for generalized sampling for WSS signals if sampling is performed in the graph frequency domain. The effectiveness of our approach is validated via experiments by comparing its MSE with existing approaches.

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“…Otherwise, (10) gives a least squares solution. While this paper focuses on the case that the signal subspace is known, we can recover signals without the exact knowledge of A with appropriate priors such as smoothness and stochastic priors [17,20,21,28]. Here we show an example of the bandlimited signal model.…”

Section: Generalized Sampling For Graph Signalsmentioning

confidence: 99%

Design of Graph Signal Sampling Matrices for Arbitrary Signal Subspaces

Hara

Yamada

Ono

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose a design method of sampling matrices for graph signals that guarantees perfect recovery for arbitrary graph signal subspaces. When the signal subspace is known, perfect reconstruction is always possible from the samples with an appropriately designed sampling matrix. However, most graph signal sampling methods so far design sampling matrices based on the bandlimited assumption and sometimes violates the perfect reconstruction condition for the other signal models. In this paper, we formulate an optimization problem for the design of the sampling matrix that guarantees perfect recovery, thanks to a generalized sampling framework for standard signals. In experiments with various signal models, our sampling matrix presents better reconstruction accuracy both for noiseless and noisy situations.

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Generalized Graph Spectral Sampling with Stochastic Priors

Cited by 9 publications

References 23 publications

Sampling Signals on Graphs: From Theory to Applications

Sampling Signals on Graphs: From Theory to Applications

Graph Signal Sampling Under Stochastic Priors

Design of Graph Signal Sampling Matrices for Arbitrary Signal Subspaces

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