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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A priorconditioned LSQR algorithm for linear ill-p
osed problems with edge-preserving regularization
- Betcke\, M (University College London)
DTSTART;TZID=Europe/London:20140207T114500
DTEND;TZID=Europe/London:20140207T121500
UID:TALK50708AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/50708
DESCRIPTION:Co-authors: Simon Arridge (University College Lond
on)\, Lauri Harhanen (Aalto University) \n\nIn thi
s talk we present a method for solving large-scale
linear inverse problems regularized with a nonlin
ear\, edge-preserving penalty term such as e.g. to
tal variation or PeronaMalik. In the proposed sche
me\, the nonlinearity is handled with lagged diffu
sivity fixed point iteration which involves solvin
g a large-scale linear least squares problem in ea
ch iteration. The size of the linear problem calls
for iterative methods e.g. Krylov methods which a
re matrix-free i.e. the forward map can be defined
through its action on a vector. Because the conve
rgence of Krylov methods for problems with discont
inuities is notoriously slow\, we propose to accel
erate it by means of priorconditioning. Priorcondi
tioning is a technique which embeds the informatio
n contained in the prior (expressed as a regulariz
er in Bayesian framework) directly into the forwar
d operator and hence into the solution space. We d
erive a factorization-free priorconditioned LSQR a
lgorithm\, allowing implicit ap plication of the p
reconditioner through efficient schemes such as mu
ltigrid. We demonstrate the effectiveness of the p
roposed scheme on a three-dimensional problem in f
luorescence diffuse optical tomography using algeb
raic multigrid preconditioner.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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