A nonlinear approach to generalized sampling
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If you have a question about this talk, please contact Martin Taylor.
One of the central problems of sampling theory is the reconstruction of an
image or a signal from a collection of measurements. Typically, this
problem may be modeled in a Hilbert space setting and measurements are
taken with respect to some set of vectors, such as some Fourier basis.
Generalized sampling is a framework for obtaining reconstructions in
arbitrary spaces without constraints on the type of measurements. In my
talk, I will present generalized sampling as an l^1 minimization problem
and apply this framework to the reconstruction of wavelets coefficients
from Fourier samples. I will also briefly discuss some implications of
generalized sampling for the use of variable density sampling schemes in
compressed sensing.
This talk is part of the Cambridge Analysts' Knowledge Exchange (C.A.K.E.) series.
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