Theory and Practice for Topological Filters
Tuesday, March 4, 2014 - 2:00pm - 2:50pm
Recently, sheaves have become useful for addressing problems in signal processing. Morphisms between sheaves provide a handy formal construct for understanding the relationship between measurements, intermediate data, and processed outputs. The resulting topological filters generalize the linear filters that engineers use extensively, but also describe novel, nonlinear filters. Because they are built from sheaves, the local structure of these filters can be tailored easily and may provide a solid theoretical grounding for nonlinear matched filters. I'll exhibit some recent results of data processed using these techniques including wind field extraction from satellite imagery.