  A new notion in frame theory, so called weaving frames has been recently
introduced to deal with some problems in signal processing and wireless sensor
networks. Also, fusion frames are an important extension of frames, used in
many areas especially for wireless sensor networks. In this paper, we survey
the notion of weaving Hilbert space fusion frames. This concept can be had
potential applications in wireless sensor networks which require distributed
processing using different fusion frames. Indeed, we present several approaches
for identifying and constructing of weaving fusion frames in terms of local
frames, bounded operators in Hilbert spaces and also dual fusion frames. To
this end, we present some conditions under which a fusion frame with its duals
constitute some pair of woven fusion frames. As a result, we show that Riesz
fusion bases are woven with all of their duals. Finally, we obtain some new
results on fusion frames and weaving fusion frames under operator
perturbations.
