Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalable $M$-Channel Critically Sampled Filter Banks for Graph Signals   We investigate a scalable $M$-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. For analysis, the graph signal is
filtered on each subband and downsampled on a corresponding set of vertices.
However, the classical synthesis filters are replaced with interpolation
operators. For small graphs, we use a full eigendecomposition of the graph
Laplacian to partition the graph vertices such that the $m^{th}$ set comprises
a uniqueness set for signals supported on the $m^{th}$ subband. The resulting
transform is critically sampled, the dictionary atoms are orthogonal to those
supported on different bands, and graph signals are perfectly reconstructable
from their analysis coefficients. We also investigate fast versions of the
proposed transform that scale efficiently for large, sparse graphs. Issues that
arise in this context include designing the filter bank to be more amenable to
polynomial approximation, estimating the number of samples required for each
band, performing non-uniform random sampling for the filtered signals on each
band, and using efficient reconstruction methods. We empirically explore the
joint vertex-frequency localization of the dictionary atoms, the sparsity of
the analysis coefficients for different classes of signals, the reconstruction
error resulting from the numerical approximations, and the ability of the
proposed transform to compress piecewise-smooth graph signals. The proposed
filter bank also yields a fast, approximate graph Fourier transform with a
coarse resolution in the spectral domain.

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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci