Deterministic and Randomized Diffusion Based Iterative Generalized Hard Thresholding (DiFIGHT) for Distributed Recovery of Sparse Signals

Abstract

In this paper, we propose a distributed iterative hard thresholding algorithm, namely, DiFIGHT, for a network that uses diffusion as the means of intra-network collaboration. Subsequently, we present a modification of the proposed algorithm, namely, MoDiFIGHT, that has lesser communication complexity than DiFIGHT. We additionally propose four different strategies, namely, RP, RNP, RGPr, and RGNPr that are used to randomly select a subset of nodes for taking part in DiFIGHT/MoDiFIGHT. This gives rise to further reduction in the mean number of communications during the run of the proposed distributed algorithms. We present theoretical estimates of the long run communication per unit time, both for DiFIGHT and MoDiFIGHT, with and without random selection of nodes. Also, we present theoretical 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 with and without random selections, the proposed algorithms exhibit performances far superior to the consensus based distributed IHT algorithm.