Applied and Computational Math Seminar: Spatially Distributed Parameters in Image Processing: From Total Variation to Fractional Models

Speaker: Carlos Rautenberg, George Mason University
Title: Spatially Distributed Parameters in Image Processing: From Total Variation to Fractional Models

Abstract: In this talk we consider recent advancements in spatially variant regularization of variational models for image processing. We focus on two main classes of problems: weighted total variation (WTV) and spatially variant fractional models. We consider formulations in function space, analyze existence, uniqueness, and stability of solutions, and provide solution algorithms together with numerical tests. For both models, we establish parameter selection rules arising from noise statistics or from rough edge detection mechanisms. In the WTV case, Fenchel duality results and consistency of solution methods are proven on the base of density of convex intersections. In the fractional case, the analysis of the problem requires the use of non-Muckenhoupt weighted Sobolev spaces and non-standard trace results are derived. We finalize the talk with several open problems and possible research directions. 

Time: Friday, September 13, 2019, 1:30-2:30pm

Place: Exploratory Hall, Room 4106