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In this paper we propose a distributed iterated hard thresholding algorithmtermed DiFIGHT over a network that is built on the diffusion mechanism and alsopropose a modification of the proposed algorithm, termed MoDiFIGHT, that haslow complexity in terms of communication in the network. We additionallypropose four different strategies termed RP, RNP, RGP$_r$, and RGNP$_r$ thatare used to randomly select a subset of nodes that are subsequently activatedto take part in the distributed algorithm, so as to reduce the mean number ofcommunications during the run of the distributed algorithm. We presenttheoretical estimates of the long run communication per unit time for thesedifferent strategies, when used by the two proposed algorithms. Also, wepresent analysis of the two proposed algorithms and provide provable bounds ontheir recovery performance with or without using the random node selectionstrategies. Finally we use numerical studies to show that both when the randomstrategies are used as well as when they are not used, the proposed algorithmsdisplay performances far superior to distributed IHT algorithm using consensusmechanism .

Deterministic and Randomized Diffusion based Iterative Generalized Hard Thresholding (DiFIGHT) for Distributed Sparse Signal Recovery