## 諸分野のための数学研究会

開催情報 火曜日　10:30～11:30　数理科学研究科棟(駒場) 056号室 儀我美一、石村直之(中央大学)、齊藤宣一、山本昌宏 http://coe.math.sci.hokudai.ac.jp/sympo/various/ 北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)の情報が掲載されております。

### 2015年09月08日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室
Monika Muszkieta 氏 (Wroclaw University of Technology)
Duality based approaches to total variation-like flows with applications to image processing (English)
[ 講演概要 ]
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.