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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Preconditioned and accelerated Douglas-Rachford al
gorithms for the solution of variational imaging p
roblems - Kristian Bredies (University of Graz)
DTSTART;TZID=Europe/London:20170905T120000
DTEND;TZID=Europe/London:20170905T125000
UID:TALK77841AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/77841
DESCRIPTION:Co-author: Hongpeng Sun (Renmin University
of China)
We present p
reconditioned and accelerated versions of the Doug
las-Rachford (DR) splitting method for the solutio
n of convex-concave saddle-point problems which of
ten arise in variational imaging. The methods enab
le to replace the solution of a linear system in e
ach iteration step in the corresponding DR iterati
on by approximate solvers without the need of cont
rolling the error. These iterations are shown to c
onverge in Hilbert space under minimal assumptions
on the preconditioner and for any step-size. More
over\, ergodic sequences associated with the itera
tion admit at least a <
img alt="" src="http://www-old.newton.ac.uk/js/Mat
hJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/1
41/0028.png"> convergence rate in te
rms of restricted primal-dual gaps. Further\, stro
ng convexity of one or both of the involved functi
onals allow for acceleration strategies that yield
improved rates of
and <
img alt="" src="http://www-old.newton.ac.uk/js/Mat
hJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/1
41/0029.png"> for \, respectively.
T
he methods are applied to non-smooth and convex va
riational imaging problems. We discuss denoising
and deconvolution with and discrepancy and total variation (TV)
as well as total generalized variation (TGV) pena
lty. Preconditioners which are specific to these
problems are presented\, the results of numerical
experiments are shown and the benefits of the res
pective preconditioned iterations are discussed.
span>
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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