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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Krylov Subspace Methods for Sparse Reconstruction
- Silvia Gazzola (University of Bath)
DTSTART;TZID=Europe/London:20171102T090000
DTEND;TZID=Europe/London:20171102T095000
UID:TALK94348AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/94348
DESCRIPTION:Krylov subspace methods are popular numerical line
ar algebra tools that can be successfully employed
to regularize linear large-scale inverse problems
\, such as those arising in image deblurring and c
omputed tomography. Though they are commonly used
as purely iterative regularization methods (where
the number of iterations acts as a regularization
parameter)\, they can be also employed in a hybrid
fashion\, i.e.\, to solve Tikhonov regularized pr
oblems (where both the number of iterations and an
d the Tikhonov parameter play the role of regulari
zations parameters\, which can be chosen adaptivel
y). Krylov subspace methods can naturally handle u
nconstrained penalized least squares problems. The
goal of this talk is to present a common framewor
k that exploits a flexible version of well-known K
rylov methods such as CGLS and GMRES to handle non
negativity constraints and regularization terms ex
pressed with respect to the 1-norm\, resulting in
an efficient way to enforce sparse reconstructions
of the solution. Numerical experiments and compar
isons with other well-known methods for the comput
ation of nonnegative and sparse solutions will be
presented. These results have been obtained workin
g jointly with James Nagy (Emory University)\, Pao
lo Novati (University of Trieste)\, Yves Wiaux (He
riot-Watt University)\, and Julianne Chung (Virgin
ia Polytechnic Institute and State University).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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