Joint design of compressed sensing (CS) and network coding (NC) has been demonstrated to provide a new data gathering paradigm for multi-hop wireless sensor networks (WSNs). By exploiting the correlation of the network sensed data, a variety of data gathering schemes based on NC and CS (Compressed Data Gathering—CDG) have been proposed. However, these schemes assume that the sparsity of the network sensed data is constant and the value of the sparsity is known before starting each data gathering epoch, thus they ignore the variation of the data observed by the WSNs which are deployed in practical circumstances. In this paper, we present a complete design of the feedback CDG scheme where the sink node adaptively queries those interested nodes to acquire an appropriate number of measurements. The adaptive measurement-formation procedure and its termination rules are proposed and analyzed in detail. Moreover, in order to minimize the number of overall transmissions in the formation procedure of each measurement, we have developed a NP-complete model (Maximum Leaf Nodes Minimum Steiner Nodes—MLMS) and realized a scalable greedy algorithm to solve the problem. Experimental results show that the proposed measurement-formation method outperforms previous schemes, and experiments on both datasets from ocean temperature and practical network deployment also prove the effectiveness of our proposed feedback CDG scheme.
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