  Distributed Compressive Sensing (DCS) improves the signal recovery
performance of multi signal ensembles by exploiting both intra- and
inter-signal correlation and sparsity structure. However, the existing DCS was
proposed for a very limited ensemble of signals that has single common
information \cite{Baron:2009vd}. In this paper, we propose a generalized DCS
(GDCS) which can improve sparse signal detection performance given arbitrary
types of common information which are classified into not just full common
information but also a variety of partial common information. The theoretical
bound on the required number of measurements using the GDCS is obtained.
Unfortunately, the GDCS may require much a priori-knowledge on various inter
common information of ensemble of signals to enhance the performance over the
existing DCS. To deal with this problem, we propose a novel algorithm that can
search for the correlation structure among the signals, with which the proposed
GDCS improves detection performance even without a priori-knowledge on
correlation structure for the case of arbitrarily correlated multi signal
ensembles.
