BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Preconditioned and accelerated Douglas-Rachford algorithms for the solution of variational imaging problems - Kristian Bredies (University o f Graz) DTSTART:20170905T110000Z DTEND:20170905T115000Z UID:TALK77841@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:Co-author: Hongpeng Sun (Renmin University of China)

We present preconditioned and accelerated versio ns of the Douglas-Rachford (DR) splitting method for the solution of conve x-concave saddle-point problems which often arise in variational imaging. The methods enable to replace the solution of a linear system in each iter ation step in the corresponding DR iteration by approximate solvers withou t the need of controlling the error. These iterations are shown to converg e in Hilbert space under minimal assumptions on the preconditioner and for any step-size. Moreover\, ergodic sequences associated with the iteration admit at least a

convergence rate in terms of restricted primal-dual gaps. Further\, strong convexity of on e or both of the involved functionals allow for acceleration strategies th at yield improved rates of

and

for

\, respectively.

The methods are applied to non-smooth a nd convex variational imaging problems. We discuss denoising and deconvol ution with

and

discrepancy and t otal variation (TV) as well as total generalized variation (TGV) penalty. Preconditioners which are specific to these problems are presented\, the results of numerical experiments are shown and the benefits of the respe ctive preconditioned iterations are discussed.
LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR