Modified distributed iterative hard thresholding

In this paper, we suggest a modified distributed compressed sensing (CS) approach based on the iterative hard thresholding (IHT) algorithm, namely, distributed IHT (DIHT). Our technique improves upon a recently proposed DIHT algorithm in two ways. First, for sensing matrices with i.i.d. Gaussian entries, we suggest an efficient and tight method for computing the step size μ in IHT based on random matrix theory. Second, we improve upon the global computation (GC) step of DIHT by adapting this step to allow for complex data, and reducing the communication cost. The new GC operation involves solving a Top-K problem and is therefore referred to as GC.K. The GC.K-based DIHT has exactly the same recovery results as the centralized IHT given the same step size μ. Numerical results show that our approach significantly outperforms the modified thresholding algorithm (MTA), another GC algorithm for DIHT proposed in previous work. Our simulations also verify that the proposed method of computing μ renders the performance of DIHT close to the oracle-aided approach with a given “optimal” μ.