Short note on phase retrievable weaving fusion frames

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.