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Fusion frames and the restricted isometry property. (English) Zbl 1254.42038

The goal of this paper is to use tools from compressed sensing, namely matrices with the restricted isometry property (RIP), to construct fusion frames with very strong properties. The authors first show that nearly tight fusion frames may be constructed, that still have the RIP property. Then, they construct fusion frames with additional strong properties, such as being nearly equi-isoclinic. Finally, they show how to replace subsets in their RIP family with orthonormal sequences while tracking the change in the RIP constants.

MSC:

42C15 General harmonic expansions, frames
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