Abstract: A primal-dual algorithm for TV-type image restoration is analyzed and
tested.
Analytically it turns out that employing a global -regularization,
with
, 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
-norm, with
, and a smooth function. In
the case
, 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
Mar. 3: Bernd Simeon, Center of Mathematics, Munich University of Technology, Germany.
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.