Multiresolution graph signal processing via circulant structures

Ekambaram, Venkatesan N.; Fanti, Giulia; Ayazifar, Babak; Ramchandran, Kannan

doi:10.1109/dsp-spe.2013.6642575

Cited by 23 publications

(16 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equivalently, we can define a circulant graph based on how it is constructed. A graph is circulant with respect to a generating set S = { Sl,S2, ... ,SM} , where o < Sk :s: N -1 , whenever there is an edge connecting the node pair ( i , ( i + S k ) mod N), for every Sk E S. In previous work, we defined fundamental signal processing operations on circulant graphs, analyzed their spectral properties, and drew certain extensions to noncirculant graphs [8] [12].…”

Section: S = {La}mentioning

confidence: 99%

“…This can be applied successively to the downsampled graph in both the HP and LP branches. The sampling procedure and the reconstruction of the downsampled graph are described in [8]. However, the filters place a restriction on neither the sampling pattern nor the construction of the downsampled graph.…”

Section: S = {La}mentioning

confidence: 99%

“…Early work on multiresolution analysis of graph signals spans diffusion wavelets [3], lifting-based basis constructions [4] [5], tree based constructions [6], spectral graph wavelets [2], quadrature mirror filters for bipartite graphs [7], and constructions based on lattice structures [8]. Researchers who study sensor networks have defined localized filters for multi scale representations [9].…”

Section: Introductionmentioning

confidence: 99%

“…Each wavelet design has advantages and disadvantages. Some constructions are oversampled representations [3] [2]; others are specialized to certain classes of graphs [7] [6]; and some require graph simplification or decomposition [5] [8].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Critically-sampled perfect-reconstruction spline-wavelet filterbanks for graph signals

Ekambaram¹,

Fanti²,

Ayazifar³

et al. 2013

2013 IEEE Global Conference on Signal and Information Processing

Self Cite

View full text Add to dashboard Cite

Inspired by first-order spline wavelets in classical signal processing, we introduce two-channel (low-pass and high-pass), critically sampled, perfect-reconstruction filterbanks for signals defined on cir culant graphs, which accommodate linear shift-invariant filtering. We then generalize to filters that process signals defined on noncirculant graphs. We apply these filters, which can be tuned to approximate desired frequency responses, to signals defined on synthetic graphs and examine their performance.

show abstract

Section: S = {La}mentioning

confidence: 99%

Section: S = {La}mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Critically-sampled perfect-reconstruction spline-wavelet filterbanks for graph signals

Ekambaram¹,

Fanti²,

Ayazifar³

et al. 2013

2013 IEEE Global Conference on Signal and Information Processing

Self Cite

View full text Add to dashboard Cite

show abstract

“…Two most commonly used DR schemes for graph signals are sampling [6]- [9] and coarsening [10]- [13]. The former performs DR for only signal on the graph and retains the graph structure; the later does a joint DR for both graph and signal.…”

Section: Introductionmentioning

confidence: 99%

Optimizing spectral diversity for graph signal coarsening

Liu

Wang

2015

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

View full text Add to dashboard Cite

Graph signal coarsening (GSC) is a kind of dimensionality reduction in irregular domain, where a coarser version of the signal and that of the underlying graph are obtained at the same time. In this paper, we propose spectral diversity for the first time for measuring the similarity between graph signals. The problem of optimizing spectral diversity for graph signal coarsening is studied, showing that the spectrum of the coarsened graph should be a subset of that of the original one. A new GSC method is then proposed, utilizing a greedy method for spectrum selection and an ADMM-based approach for graph signal acquisition. Numerical experiments demonstrate that the proposed method performs better than available reference algorithms.

show abstract

A Modified Spline Graph Filter Bank

Miraki

Saeedi-Sourck

2020

Circuits Syst Signal Process

View full text Add to dashboard Cite

In this paper, we present a structure for two-channel spline graph filter bank with spectral sampling (SGFBSS) on arbitrary undirected graphs. Our proposed structure has many desirable properties; namely, perfect reconstruction, critical sampling in spectral domain, flexibility in choice of shape and cutoff frequency of the filters, and low complexity implementation of the synthesis section, thanks to our closed-form derivation of the synthesis filter and its sparse structure. These properties play a pivotal role in multi-scale transforms of graph signals. Additionally, this framework can use both normalized and nonnormalized Laplacian of any undirected graph. We evaluate the performance of our proposed SGFBSS structure in nonlinear approximation and denoising applications through simulations. We also compare our method with the existing graph filter bank structures and show its superior performance.

show abstract

Multiresolution graph signal processing via circulant structures

Cited by 23 publications

References 15 publications

Critically-sampled perfect-reconstruction spline-wavelet filterbanks for graph signals

Critically-sampled perfect-reconstruction spline-wavelet filterbanks for graph signals

Optimizing spectral diversity for graph signal coarsening

A Modified Spline Graph Filter Bank

Contact Info

Product

Resources

About