Speaker: Matthew Fickus (Air Force Institute of Technology)

Title: Constructions and existence of tight fusion frames


Fusion frames are an emerging topic of frame theory, with applications to encoding and distributed sensing. However, little is known about the existence of tight fusion frames, and even less is known about how to construct them. We discuss how fusion frames may be regarded as special cases of traditional frames, rather than generalizations of them. This perspective paves the way for a harmonic frame-inspired construction of tight fusion frames, as well as two distinct methods for producing tight fusion frames which are complementary to an existing one. This perspective further permits one to characterize tight fusion frames as the minimizers of a fusion frame potential. Despite this work, many basic questions regarding the existence and construction of tight fusion frames remain open.