Fast pursuit method for greedy algorithms in Distributed Compressive Sensing

This paper proposes a fast pursuit method for greedy algorithms when reconstructing multi-signals under Distributed Compressive Sensing (DCS) framework. DCS takes advantage of both intra- and inter-signal correlation structures to reduce the measurements required for signals recovery. Greedy algorithms, much faster than l₀ and l₁ minimization algorithms, are widely used in DCS. General approaches transform DCS model to Compressive Sensing (CS) model and then directly use greedy algorithms to reconstruct signals, but the recovery speed becomes very slow as the signal number n increasing. In this paper, we propose a fast pursuit method which exploits the structural features of joint measurement matrix to reduce the computational complexity form O(n²) to O(n) when calculating inner-product in greedy algorithms, which improves the recovery speed significantly without reducing recovery accuracy.