Traditional signal processing
deals with signals which are
defined on well-structured grids
(e.g., Cartesian grids for
images and videos or time-lines
for time signals) and has been
very successful in developing
theories and methods to extract
salient information from these
well-ordered types of data. At
the same time, data stored and
shared in real-world complex
systems (e.g., social networks,
sensor networks, etc.) can be
conveniently modelled as
high-dimensional signals
residing on the vertices of
graphs, in which links are
established based on
connectivity and/or similarity.
Graphical models have been
extensively studied in the past,
however, traditional approaches
fail to encapsulate the many
properties of the signals
defined on graphs.
The goal of this project is to
advance the theory of signal
processing on graphs with the
aim of merging graph theoretic
concepts such as graph
laplacian, graph clustering,
node centrality with concepts in
computational harmonic analysis
such as compact or sparse signal
representation, approximation
and dimensionality reduction in
order to devise new tools and
algorithms for the intelligent
management of large amounts
of data available over
complex networks such as social
networks. In particular, we aim
to advance the theory of
wavelets on graphs with
particular emphasis on the
extension of the notion of
polynomial and exponential
splines for signals defined on
graphs.
