The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains

Shuman, David I; Narang, Sunil K.; Frossard, Pascal; Ortega, Antonio; Vandergheynst, Pierre

doi:10.1109/msp.2012.2235192

Cited by 3,630 publications

(3,174 citation statements)

References 56 publications

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“…With the increased interest in graph approaches to data analysis, a great amount of research has been devoted to generalizing signal processing operations to the graph setting (Shuman et al, 2013). This includes wavelet transforms, with the spectral graph wavelet transform (SGWT) proposed in Hammond et al (2011) being an example.…”

Section: Introductionmentioning

confidence: 99%

Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping

et al. 2015

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A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graph wavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar gray matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity.

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Section: Introductionmentioning

confidence: 99%

Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping

et al. 2015

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“…In general graph signal processing [3], an undirected graph G = (V, E) consists of a collection of nodes V = {1, 2, ..., N } connected by a set of links E = {(i, j, w ij )},i, j ∈ V where (i, j, w ij ) denotes the link between nodes i and j having weights w ij . For image processing applications, a pixel may be treated as a node in a graph.…”

Section: Basics Of Images On Graphsmentioning

confidence: 99%

“…In recent years, the emerging graph signal processing tools have been applied to classical image processing tasks [3]. For example, a typical interpolation problem was studied using spectral graph theory in [4], where the upsampling problem is formulated as a regularized least squares problem.…”

Section: Introductionmentioning

confidence: 99%

Depth-assisted stereo video enhancement using graph-based approaches

Tian

Mansour

Vetro

et al. 2014

2014 IEEE International Conference on Image Processing (ICIP)

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In stereo video applications, the quality of the two views may vary based on different camera capturing conditions and setup, compression/transmission, and sensor noise. Although some studies show that the perceived video quality may not be significantly affected by the lower quality view, maintaining a similar video quality is still desired in order to prevent eye strain during extended viewing sessions. In this paper, we study a graph-based approach to enhance the lower quality views by referring to the high quality view in addition to an accompanying depth map. We construct a graphical signal model with joint bilateral edge weights and show that graph-based joint bilateral filtering can better suppress several types of noises, e.g., Gaussian, motion as well as quantization noise. IEEE International Conference on Image Processing (ICIP)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. ABSTRACTIn stereo video applications, the quality of the two views may vary based on different camera capturing conditions and setup, compression/transmission, and sensor noise. Although some studies show that the perceived video quality may not be significantly affected by the lower quality view, maintaining a similar video quality is still desired in order to prevent eye strain during extended viewing sessions. In this paper, we study a graph-based approach to enhance the lower quality views by referring to the high quality view in addition to an accompanying depth map. We construct a graphical signal model with joint bilateral edge weights and show that graph-based joint bilateral filtering can better suppress several types of noises, e.g., Gaussian, motion as well as quantization noise.Index Terms-3D video, graph-based filtering, graphbased joint bilateral filtering (GB-JBF)

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“…Coping with the needs posed by fields such as network science and big data requires extending the results existing for classical timevarying signals to signals defined on graphs [1], [2]. 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.…”

Section: Introductionmentioning

confidence: 99%

“…Then, we analyze the reconstruction performance when noisy signals in real-world networks are considered. 1 …”

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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The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains

Cited by 3,630 publications

References 56 publications

Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping

Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping

Depth-assisted stereo video enhancement using graph-based approaches

Reconstruction of graph signals: Percolation from a single seeding node

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