Weaving Hilbert Space Frames and Duality

TL;DR

This paper surveys the theory of weaving Hilbert space frames, focusing on duality principles, and introduces new properties and conditions for dual frames to form woven frames, including stability under perturbations.

Contribution

It provides new insights into duality in weaving frames, including sufficient conditions for dual pairs to be woven, and reviews stability aspects under various perturbations.

Findings

Sufficient conditions for dual frames to be woven.

New properties related to duality in weaving frames.

Analysis of stability under perturbations.

Abstract

Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new properties in weaving frame theory related to dual frames. Specifically, we give some sufficient conditions under which a frame with its canonical dual, alternate duals or approximate duals constitute some concrete pairs of woven frames. Moreover, we survey the stability of weaving frames under perturbations and different operators.