Fusion Frames and the Restricted Isometry Property

TL;DR

This paper explores how tight frames with the restricted isometry property can generate nearly tight fusion frames that are nearly orthogonal and equi-isoclinic, and discusses replacing parts of these frames with orthonormal sets.

Contribution

It introduces methods to construct nearly tight fusion frames from RIP frames and shows how to replace parts with orthonormal sets without losing the RIP property.

Findings

RIP frames lead to nearly tight fusion frames

Fusion frames are nearly orthogonal and equi-isoclinic

Replacing parts with orthonormal sets preserves RIP

Abstract

We will show that tight frames satisfying the restricted isometry property give rise to nearly tight fusion frames which are nearly orthogonal and hence are nearly equi-isoclinic. We will also show how to replace parts of the RIP frame with orthonormal sets while maintaining the RIP property.