Short note on phase retrievable weaving fusion frames

TL;DR

This paper explores the theoretical properties of phase retrievable weaving fusion frames, highlighting their robustness and potential in signal reconstruction, with an application to probabilistic erasure.

Contribution

It provides new characterizations and insights into the structure of phase retrievable weaving fusion frames, extending foundational work in the field.

Findings

Enhanced redundancy and stability in signal reconstruction

Deeper understanding of fusion frame structure

Application to probabilistic erasure scenarios

Abstract

Fusion frames are extensively studied due to their effectiveness in recovering signals from large-scale data. They are applicable in distributed processing, wireless sensor networks, and packet encoding systems due to their robustness and redundancy. Motivated by the foundational work of Bemrose et al.\cite{Be16} and Balan\cite{Ba13}, this paper investigates the theoretical properties and characterizations of phase retrievable weaving fusion frames. These frames offer enhanced redundancy and stability in signal reconstruction. We present key results that deepen the understanding of their structure and behaviour. Lastly, an application involving probabilistic erasure is explored to demonstrate their practical utility.