Sampling
and Reconstruction driven by
Sparsity Models with
Applications in Sensor
Networks and
Neuroscience
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The problem of reconstructing
or estimating partially observed
or sampled signals is an
important one that finds
application in many areas of
signal processing and
communications. Traditional
acquisition and reconstruction
approaches are heavily
influences by classical Shannon
sampling theory which gives an
exact sampling and interpolation
formula for bandlimited signals.
Recently, the emerging theory of
sparse sampling has challenged
the way we think about signal
acquisition and has demonstrated
that, by using more
sophisticated signal models, it
is possible to break away from
the need to sample signals at
the Nyquist rate. The insight
that sub-Nyquist sampling can,
under some circumstances, allow
perfect reconstruction is
revolutionizing signal
processing, communications and
inverse problems. Given the
ubiquity of the sampling
process, the implications of
these new research developments
are far reaching.
This project is based on the
applicant’s recent work on the
sampling of sparse
continuous-time signals and aims
to extend the existing theory to
include more general signal
models that are closer to the
physical characteristics of real
data, to explore new domains
where sparsity and sampling can
be effectively used and to
provide a set of new fast
algorithms with clear and
predictable performance. As part
of this work, he will also
consider timely important
problems such as the
localization of diffusive
sources in sensor networks and
the analysis of neuronal signals
of the brain. He will, for the
first time, pose these as sparse
sampling problems and in this
way he expects to develop
technologies with a step change
in performance.
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