The talk On a Parabolic-Hyperbolic Filter for Image Processing, by Michael Pokojovy (Charles University in Prague), will be held on Monday February 29, 2016 at 9:00 in room K6.
We propose a novel PDE-based anisotropic filter for multicolor image denoising. Our filter can be viewed as a hyperbolic relaxation of the well-known parabolic Perona & Malik filter (1990). First, we consider a mollifier-type regularization of our PDE system and exploit the L2-maximal regularity theory for non-autonomous forms to prove a well-posedness result both in the weak and the strong settings. Based on an a fixed point argument, the existence and uniqueness of strong solutions for the original quasilinear problem are also obtained and their long-time behavior is studied.