The Effect of Perturbations of Frames and Fusion Frames on Their Redundancies

TL;DR

This paper explores how perturbations affect the redundancies of frames and fusion frames, establishing relationships and expressing redundancies through cosine angles between subspaces.

Contribution

It introduces new relationships between perturbed frames and their redundancies, linking these to cosine angles between subspaces.

Findings

Redundancy relations are established for perturbed frames and fusion frames.

Redundancy can be expressed via cosine angles between subspaces.

Perturbation effects on frame properties are characterized.

Abstract

An interesting question about the perturbed sequences is: when do they inherit the properties of the original one? An elegant relation between frames (fusion frames) and their perturbations is the relation of their redundancies. In this paper, we investigate these relationships. Also, we express the redundancy of frames (fusion frames) in terms of the cosine angle between some subspaces.