Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs

@article{Narang2012CompactSB,
  title={Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs},
  author={Sunil K. Narang and Antonio Ortega},
  journal={IEEE Transactions on Signal Processing},
  year={2012},
  volume={61},
  pages={4673-4685}
}
This paper extends previous results on wavelet filterbanks for data defined on graphs from the case of orthogonal transforms to more general and flexible biorthogonal transforms. As in the recent work, the construction proceeds in two steps: first we design “one-dimensional” two-channel filterbanks on bipartite graphs, and then extend them to “multi-dimensional” separable two-channel filterbanks for arbitrary graphs via a bipartite subgraph decomposition. We specifically design wavelet filters… 
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199 Citations
Highly Influential Citations
28
Background Citations
95
Methods Citations
67
Results Citations
3

199 Citations

Spectral Folding And Two-Channel Filter-Banks On Arbitrary Graphs

A different definition of the graph Fourier transform (GFT), where orthogonality is defined with respect to the Q inner product, is constructed, which allows to easily construct orthogonal and bi-orthogonal perfect reconstruction filter-banks.

Techniques for Constructing Biorthogonal Bipartite Graph Filter Banks

It is shown that filters having virtual spectral symmetry and almost energy preservation can be constructed without any sophisticated optimization, and fine control of the spectral response can also be achieved with ease.

Subgraph-Based Filterbanks for Graph Signals

A critically sampled compact-support biorthogonal transform for graph signals, via graph filterbanks, based on a partition of the graph in connected subgraphs, which applies successfully to decompose graph signals and shows promising performance on compression and denoising.

Critical sampling for wavelet filterbanks on arbitrary graphs

  • Aamir AnisAntonio Ortega
  • Mathematics
    2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2017
A critical sampling scheme on an arbitrary graph that chooses a sampling set for each channel, given a set of analysis/synthesis filters, by seeking to minimize a bound on the overall reconstruction error associated with the filterbank is proposed.

Bipartite Approximation for Graph Wavelet Signal Decomposition

This paper designs new bipartite approximation strategies for model-based and empirically derived probability distributions and proposes a local heuristic approach for fast implementation with simplifications leading to local metric computation.

Design of Two Channel Biorthogonal Graph Wavelet Filter Banks with Half-Band Kernels

  • Xi Zhang
  • Engineering
    IEICE Trans. Fundam. Electron. Commun. Comput. Sci.
  • 2017
This paper uses the polynomial half-band kernels to construct a class of biorthogonal graph wavelet filter banks, which exactly satisfy the PR (perfect reconstruction) condition and applies the Remez exchange algorithm to minimize the spectral error of lowpass (highpass) filter in the band of interest by using the remaining degree of freedom.

Two Channel Filter Banks on Arbitrary Graphs with Positive Semi Definite Variation Operators

—We propose novel two-channel filter banks for sig- nals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex…

Tree-structured filter banks for M-block cyclic graphs

This work considers a simpler setting where M is a power of 2 and proposes a perfect reconstruction tree-structured biorthogonal filter bank solution comprised of a hierarchical 2-channel design.

An M-channel critically sampled filter bank for graph signals

  • Yan JinD. Shuman
  • Computer Science
    2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2017
An M-channel critically sampled filter bank for graph signals where each of the M filters is supported on a different subband of the graph Laplacian spectrum is investigated, and graph signals are perfectly reconstructable from their analysis coefficients.

Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs

—In this paper, we propose the construction of critically sampled perfect reconstruction two-channel filterbanks on arbitrary undirected graphs. Inspired by the design of graphQMF proposed in the…
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