  In this paper, we exploit the theory of compressive sensing to perform
detection of a random source in a dense sensor network. When the sensors are
densely deployed, observations at adjacent sensors are highly correlated while
those corresponding to distant sensors are less correlated. Thus, the
covariance matrix of the concatenated observation vector of all the sensors at
any given time can be sparse where the sparse structure depends on the network
topology and the correlation model. Exploiting the sparsity structure of the
covariance matrix, we develop a robust nonparametric detector to detect the
presence of the random event using a compressed version of the data collected
at the distributed nodes. We employ the multiple access channel (MAC) model
with distributed random projections for sensors to transmit observations so
that a compressed version of the observations is available at the fusion
center. Detection is performed by constructing a decision statistic based on
the covariance information of uncompressed data which is estimated using
compressed data. The proposed approach does not require any knowledge of the
noise parameter to set the threshold, and is also robust when the distributed
random projection matrices become sparse.
