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

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.

LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR