Woven fusion frames in Hilbert spaces

TL;DR

This paper introduces and studies woven fusion frames in Hilbert spaces, exploring their properties, perturbation effects, and Riesz decompositions to advance signal processing and data analysis techniques.

Contribution

It proposes the concept of woven fusion frames, extending the theory of frames and analyzing their stability and decomposition properties.

Findings

Woven fusion frames are effective for distributed data processing.

Perturbation analysis shows stability of woven frames under certain conditions.

Riesz decomposition provides a new perspective on woven frame structure.

Abstract

A new notion in frame theory has been introduced recently that called woven frames. %From the perspective of others, Woven and weaving frames are powerful tools for pre-processing signals and distributed data processing. The purpose of introducing fusion frame or frame of subspace is to first construct local components and then build a global frame from these. This type of frame behaves as a generalization of frames. Motivating by the concepts of fusion and weaving frames, we investigate the notion woven-weaving fusion frames and present some of their features. Also, we study some effects of perturbations on woven frames and introduce Riesz decomposition of wovens and then we examine some of behaviors of this type of decomposition.