Skip to main
Math equations

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

* The programs and services offered by George Mason University are open to all who seek them. George Mason does not discriminate on the basis of race, color, religion, ethnic national origin (including shared ancestry and/or ethnic characteristics), sex, disability, military status (including veteran status), sexual orientation, gender identity, gender expression, age, marital status, pregnancy status, genetic information, or any other characteristic protected by law. After an initial review of its policies and practices, the university affirms its commitment to meet all federal mandates as articulated in federal law, as well as recent executive orders and federal agency directives.