the Institute for Theoretical and Engineering Science
Department of Mathematics

University of Houston

Scientific Computing Seminar

Professor Michael Hintermüller
Institute of Mathematics
University of Graz, Austria

An infeasible primal-dual algorithm for
TV-based inf-convolution-type image restoration

Thursday, February 24, 2005
Room 634 S&R1

Abstract: A primal-dual algorithm for TV-type image restoration is analyzed and tested. Analytically it turns out that employing a global $L^s$-regularization, with $1< s\leq 2$, in the dual problem results in a local smoothing of the TV-regularization term in the primal problem. The local smoothing can alternatively be obtained as the infimal convolution of the $\ell_r$-norm, with $r^{-1}+s^{-1}=1$, and a smooth function. In the case $r=s=2$, this results in Gauss-TV-type image restoration. The globalized primal-dual algorithm introduced in this paper works with generalized derivatives, converges locally at a superlinear rate and is stable with respect to noise in the data. In addition, it utilizes a projection technique which reduces the size of the linear system that has to be solved per iteration. A comprehensive numerical study ends the talk.

Future talks in Scientific Computing Seminar

$\bullet$ Mar. 3: Bernd Simeon, Center of Mathematics, Munich University of Technology, Germany. $\bullet$ Apr. 28: Gene H Golub, Department of Computer Science, Stanford University.

This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.