Title: Deterministic and Randomized Diffusion based Iterative Generalized Hard Thresholding (DiFIGHT) for Distributed Sparse Signal Recovery,
Abstract: In this paper, we propose a distributed iterated hard thresholding algorithm
termed DiFIGHT over a network that is built on the diffusion mechanism and also
propose a modification of the proposed algorithm termed MoDiFIGHT, that has low
complexity in terms of communication in the network. We additionally propose
four different strategies termed RP, RNP, RGPr, and RGNPr that are used to
randomly select a subset of nodes that are subsequently activated to take part
in the distributed algorithm, so as to reduce the mean number of communications
during the run of the distributed algorithm. We present theoretical estimates
of the long run communication per unit time for these different strategies,
when used by the two proposed algorithms. Also, we present an analysis of the
two proposed algorithms and provide provable bounds on their recovery
performance with or without using the random node selection strategies.
Finally, we use numerical studies to show that both when the random strategies
are used as well as when they are not used, the proposed algorithms display
performances far superior to distributed IHT algorithm using consensus
mechanism.