Speaker: Fernando Charro Associate Professor of Mathematics, Wayne State University

Title: Digital-Image Restoration, Game Theory, and Partial Differential Equations

Absract: In this talk, we will explore some recent connections between three seemingly unrelated areas: digital-image reconstruction or inpainting, game theory, and partial differential equations (PDEs). Inpainting algorithms allow not just to restore damaged photographs, but also to remove undesired objects and writings on an image. Many popular inpainting algorithms use PDEs to repair missing or damaged pixels by interpolating information from neighboring pixels. For instance, the nearest-neighbor method replaces a corrupted pixel with the mean intensity of its neighbors. More adventurous choices involve inpainting with the median intensity of neighboring pixels or propagating from neighboring pixels. In the talk, we will discuss these imagerestoration algorithms and connect them to Random Tug-of-War games and nonlinear PDEs.