A quantitative notion of redundancy for infinite frames

TL;DR

This paper explores how the concept of quantitative redundancy, originally defined for finite frames, can be extended and applied to infinite frames in Hilbert spaces.

Contribution

It investigates the generalization of Bodmann, Casazza, and Kutyniok's redundancy notions from finite to infinite frames.

Findings

Redundancy concepts are adaptable to infinite frames.

The paper establishes conditions under which the finite frame redundancy notions extend.

Potential applications in signal processing and frame theory are discussed.

Abstract

Bodmann, Casazza and Kutyniok introduced a quantitative notion of redundancy for finite frames - which they called {\em upper and lower redundancies} - that match better with an intuitive understanding of redundancy for finite frames in a Hilbert space. The objective of this paper is to see how much of this theory generalizes to infinite frames.