Convergence of Iterative Hard Thresholding Variants with Application to Asynchronous Parallel Methods for Sparse Recovery

Recently several asynchronous parallel algorithms for sparse recovery have been proposed. These methods share an estimation of the support of the signal between nodes, which then use this information in addition to their local estimation of the support to update via an iterative hard thresholding (IHT) method. We analyze a generalized version of the IHT method run on each of the nodes and show that this method performs at least as well as the standard IHT method. We perform numerical simulations that illustrate the potential advantage these methods enjoy over the standard IHT.