Efficient sensor position selection using graph signal sampling theory

Sakiyama, Akie; Tanaka, Yuichi; Tanaka, Toshihisa; Ortega, Antonio

doi:10.1109/icassp.2016.7472874

Cited by 36 publications

(23 citation statements)

References 31 publications

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“…Even methods that were not initially viewed from a graph perspective, e.g., methods based on entropy [23], [24] and mutual information [25], [26], are included as its special cases (see Section IV). Our preliminary work [27], [28] partially solved the problem of sensor position selection of sensor networks [25], [29]- [31] using sampling theory for graph signals [14]- [16] and proposed a sensor selection method based on the localization operator. This paper adds many theoretical and practical implications.…”

Section: A Motivationmentioning

confidence: 99%

Eigendecomposition-Free Sampling Set Selection for Graph Signals

Sakiyama

Tanaka

et al. 2019

IEEE Trans. Signal Process.

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This paper addresses the problem of selecting an optimal sampling set for signals on graphs. The proposed sampling set selection (SSS) is based on a localization operator that can consider both vertex domain and spectral domain localization. We clarify the relationships among the proposed method, sensor position selection methods in machine learning, and conventional SSS methods based on graph frequency. In contrast to the conventional graph signal processing-based approaches, the proposed method does not need to compute the eigendecomposition of a variation operator, while still considering (graph) frequency information. We evaluate the performance of our approach through comparisons of prediction errors and execution time.

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Section: A Motivationmentioning

confidence: 99%

Eigendecomposition-Free Sampling Set Selection for Graph Signals

Sakiyama

Tanaka

et al. 2019

IEEE Trans. Signal Process.

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“…Sakiyama et al [34], [35] study node selection methods in the context of sensor position selection. In [34] an assumption of a bandlimited signal is made and nodes are selected so that the cutoff frequency of the signal restricted to the sampling set is maximized. This is done using three possible techniques requiring access to the eigenvectors of the graph Laplacian.…”

Section: Related Workmentioning

confidence: 99%

Sampling of Graph Signals via Randomized Local Aggregations

Valsesia

Fracastoro

Magli

2019

IEEE Trans. on Signal and Inf. Process. over Networks

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Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges arise and defining an efficient sampling strategy is not straightforward. Recently, several works have addressed this problem. The most common techniques select a subset of nodes to reconstruct the entire signal. However, such methods often require the knowledge of the signal support and the computation of the sparsity basis before sampling. Instead, in this paper we propose a new approach to this issue. We introduce a novel technique that combines localized sampling with compressed sensing. We first choose a subset of nodes and then, for each node of the subset, we compute random linear combinations of signal coefficients localized at the node itself and its neighborhood. The proposed method provides theoretical guarantees in terms of reconstruction and stability to noise for any graph and any orthonormal basis, even when the support is not known. Code is available at https://git.io/fj0Ib

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“…whose K largest eigenvalues are the same as λ B and the remaining eigenvalues are constants irrelevant to η. Since the first term in (13) is not related to the design, the optimal η * that maximizes (13) is the one that maximizes log det(G B (η)). Recall (14) and the analysis for non-Bayesian DoS, λ B lies within Gershgorin discs of G B (η * ) which can be obtained by changing the discs of (V K Σf K V T K ) by η * and then translating all the discs by σ 2 w .…”

Section: B Difference Between Non-bayesian and Bayesian Dosmentioning

confidence: 99%

“…The first and second-order statistics of a graph signal is required in the stochastic prior [10], [11]. For example, a stochastic graph signal may follow joint zero-mean Gaussian distribution [12], [13].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Design of Sampling Set for Bandlimited Graph Signals

Xie

Feng

et al. 2019

2019 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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The design of sampling set (DoS) for bandlimited graph signals (GS) has been extensively studied in recent years, but few of them exploit the benefits of the stochastic prior of GS. In this work, we introduce the optimization framework for Bayesian DoS of bandlimited GS. We also illustrate how the choice of different sampling sets affects the estimation error and how the prior knowledge influences the result of DoS compared with the non-Bayesian DoS by the aid of analyzing Gershgorin discs of error metric matrix. Finally, based on our analysis, we propose a heuristic algorithm for DoS to avoid solving the optimization problem directly.

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Efficient sensor position selection using graph signal sampling theory

Cited by 36 publications

References 31 publications

Eigendecomposition-Free Sampling Set Selection for Graph Signals

Eigendecomposition-Free Sampling Set Selection for Graph Signals

Sampling of Graph Signals via Randomized Local Aggregations

Bayesian Design of Sampling Set for Bandlimited Graph Signals

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