Seminar on Mathematics for various disciplines

Seminar information archive ~04/12Next seminarFuture seminars 04/13~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2015/09/08

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Monika Muszkieta (Wroclaw University of Technology)
Duality based approaches to total variation-like flows with applications to image processing (English)
[ Abstract ]
During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of di fferentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.
This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.