Common-Innovation Subspace Pursuit for Distributed Compressed Sensing in Wireless Sensor Networks

We study the sparse signal reconstruction problem in a wireless sensor network (WSN) using distributed compressed sensing. The sparse signals from multiple sensors are modeled by the mixed-support set model that characterizes the inter-correlation of the signals by the common support set and represents the individual features by the innovation support sets. A novel algorithm, namely common-innovation subspace pursuit (CISP), is proposed to estimate the common and innovation support sets separately, to reduce the reconstruction error and computing time. The proposed algorithm consists of two stages, the eigen-value decomposition-based common subspace pursuit and projection-based innovation subspace pursuit. We analyze the convergence performance of the CISP algorithm, where a bound of reconstruction error is provided. Furthermore, a range of simulations and experiments are conducted to evaluate the performance of the proposed algorithm. The results of simulations on a hierarchical clustering-based WSN show that the proposed CISP algorithm is superior over the orthogonal matching pursuit and distributed parallel pursuit algorithms in terms of both reconstruction error and runtime, in the scenario of a large-scale sensor network. Moreover, the experiments on the real data from the temperature and humidity sensors deployed in the Intel Berkeley Lab verify that, the proposed CISP algorithm is capable of reconstructing the multiple sparse signals accurately and efficiently, in the real-life application.