Miraki, Amir and Saeedi-Sourck, Hamid and Marchetti, Nicola and Farhang, Arman
(2021)
Spectral Domain Spline Graph Filter Bank.
IEEE Signal Processing Letters, 28.
pp. 469-473.
ISSN 1070-9908
Abstract
In this letter, 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 the choice of shape and cut-off
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 non-normalized
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.
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