A Survey of Fusion Frames in Hilbert Spaces

KÖHLDORFER L.; BALAZS P.; CASAZZA P.; HEINEKEN S.; HOLLOMEY C.; MORILLAS P.; SHAMSABADI M.

Sampling, Approximation, and Signal Analysis (Harmonic Analysis in the Spirit of J. Rowland Higgins)

Birkhäuser

Año: 2023; p. 245 - 328

Fusion frames are a very active area of research today because of theirmyriadof applications in pure mathematics, applied mathematics, engineering, medicine,signal and image processing and much more. They provide a great flexibility for designingsets of vectors for applications and are therefore prominent in all these areas,including e.g. mitigating the effects of noise in a signal or giving robustness to erasures.In this chapter, we present the fundamentals of fusion frame theory with anemphasis on their delicate relation to frame theory. The goal here is to provide researchersand students with an easy entry into this topic. Proofs for fusion frames willbe self-contained and differences between frames and fusion frames are analyzed.In particular, we focus on the subtleties of fusion frame duality. We also provide areproducible research implementation.