Generalized distributed compressive sensing with security challenges for linearly correlated information sources

Summary Distributed compressive sensing (DCS) usually improves the signal recovery performance of multi‐signal ensembles by exploiting both intra‐ and inter‐signal correlation and sparsity structure. However, the existing DCS had proposed for a very limited ensemble of signals that has only single common information. This paper proposes a generalized DCS (GDCS) framework which can improve sparse signal detection performance given arbitrary types of common information, which are classified into full common information and partial common information after overcoming against existing limitation. Specifically, the theoretical bound on the required number of measurements under the GDCS is obtained. We also develop a practical algorithm to obtain benefits using the GDCS. At the end of this paper, it simply summarizes the potential security issues when it gets all sensing information in a sensor network. Finally, numerical results verify that the proposed algorithm reduces the required number of measurements for correlated sparse signal detection compared to the DCS algorithm. This research lays down the basis for efficient distributed signal detection so that it can improve the detection performance or it can detect the signal reliably when the number of signal observations is limited.