Towards a sampling theorem for signals on arbitrary graphs

Anis, Aamir; Gadde, Akshay; Ortega, Antonio

doi:10.1109/icassp.2014.6854325

Cited by 182 publications

(198 citation statements)

References 19 publications

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“…More specifically, that x can be expressed as a linear combination of a subset of the columns of V = [v 1 , ..., v N ], or, equivalently, that the vector x = V −1 x is sparse [7]. In this context, vectors v i are interpreted as the graph frequency basis, x i as the corresponding signal frequency coefficients, and x as a K-bandlimited graph signal.…”

Section: Bandlimited Graph Signalsmentioning

confidence: 99%

Interpolation of graph signals using shift-invariant graph filters

Segarra

Marqués

Leus

et al. 2015

2015 23rd European Signal Processing Conference (EUSIPCO)

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New schemes to recover signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of the graph. The schemes are designed within the framework of linear shift-invariant graph filters and consider that the seeding signals are injected only at a subset of interpolating nodes. After several sequential applications of the graph-shift operator -which computes linear combinations of the information available at neighboring nodes-the seeding signals are diffused across the graph and the original bandlimited signal is eventually recovered. Conditions under which the recovery is feasible are given, and the corresponding schemes to recover the signal are proposed. Connections with the classical interpolation in the time domain are also discussed.

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Section: Bandlimited Graph Signalsmentioning

confidence: 99%

Interpolation of graph signals using shift-invariant graph filters

Segarra

Marqués

Leus

et al. 2015

2015 23rd European Signal Processing Conference (EUSIPCO)

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show abstract

“…More specifically, that x can be expressed as a linear combination of a subset of the columns of V = [v1, ..., vN ], or, equivalently, that the vector x = V −1 x is sparse [3]. In this context, vectors vi are interpreted as the graph frequency basis, xi as the corresponding signal frequency coefficients, and x as a K bandlimited graph signal.…”

Section: B Bandlimited Graph Signalsmentioning

confidence: 99%

“…This not only entails modifying the algorithms currently available for time-varying signals, but also gaining intuition on what concepts are preserved (and lost) when a signal is defined, not in the classical time grid, but in a more general graph domain. Two problems that have recently received substantial attention are sampling [3]- [6] and filtering [2] signals that are defined on the nodes of a graph.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of graph signals: Percolation from a single seeding node

Segarra

Marqués²,

Leus

et al. 2015

2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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Abstract-Schemes to reconstruct signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of the graph. The schemes, which are designed within the framework of linear shift-invariant graph filters, consider that the signal is injected at a single seeding node. After several sequential applications of the graph-shift operator -which computes linear combinations of the information available at neighboring nodes -the seeding signal percolates across the graph. We show that if the node is allowed to change the seeding signal with each application of the shift operator, the original bandlimited signal can be recovered.Conditions under which such a recovery is feasible are identified for two different reconstruction schemes. We illustrate both reconstruction schemes in synthetic graph signals and we analyze their performance in noisy real-world scenarios.

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“…We further compare the sampling complexity of the weighted S 2 algorithm with an alternative state-of-the-art method called the cutoff maximization method [4]. Unlike the S 2 methods, which aim for a complete recovery of the signal by aggressively searching for the boundary nodes, the cutoff maximization method is focused only on providing a good approximation of the signal by ensuring that the unsampled nodes are well-connected to the sampled nodes [8].…”

Section: Introductionmentioning

confidence: 99%

“…The methods with this approach [2,3] sample nodes sequentially, i.e., the nodes to be sampled next are chosen based on the graph structure as well as previously observed signal values. The second approach [4,5,6], in contrast, utilizes global properties of the graph in order to identify the most informative nodes, and sample them all at once. Such global approaches usually focus on providing a good approximation of the signal, rather than exact recovery.…”

Section: Introductionmentioning

confidence: 99%

Active learning on weighted graphs using adaptive and non-adaptive approaches

Gad

Gadde

Avestimehr

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper studies graph-based active learning, where the goal is to reconstruct a binary signal defined on the nodes of a weighted graph, by sampling it on a small subset of the nodes. A new sampling algorithm is proposed, which sequentially selects the graph nodes to be sampled, based on an aggressive search for the boundary of the signal over the graph. The algorithm generalizes a recent method for sampling nodes in unweighted graphs. The generalization improves the sampling performance using the information gained from the available graph weights. An analysis of the number of samples required by the proposed algorithm is provided, and the gain over the unweighted method is further demonstrated in simulations. Additionally, the proposed method is compared with an alternative stateof-the-art method, which is based on the graph's spectral properties. It is shown that the proposed method significantly outperforms the spectral sampling method, if the signal needs to be predicted with high accuracy. On the other hand, if a higher level of inaccuracy is tolerable, then the spectral method outperforms the proposed aggressive search method. Consequently, we propose a hybrid method, which is shown to combine the advantages of both approaches.Index Terms-active learning on graphs, adaptive and nonadaptive sampling of graph signals, sampling complexity

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Towards a sampling theorem for signals on arbitrary graphs

Cited by 182 publications

References 19 publications

Interpolation of graph signals using shift-invariant graph filters

Interpolation of graph signals using shift-invariant graph filters

Reconstruction of graph signals: Percolation from a single seeding node

Active learning on weighted graphs using adaptive and non-adaptive approaches

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