  We consider a distributed compressed sensing scenario where many sensors
measure correlated sparse signals and the sensors are connected through a
network. Correlation between sparse signals is modeled by a partial common
support-set. For such a scenario, the main objective of this paper is to
develop a greedy pursuit algorithm. We develop a distributed parallel pursuit
(DIPP) algorithm based on exchange of information about estimated support-sets
at sensors. The exchange of information helps to improve estimation of the
partial common support-set, that in turn helps to gradually improve estimation
of support-sets in all sensors, leading to a better quality reconstruction
performance. We provide restricted isometry property (RIP) based theoretical
analysis on the algorithm's convergence and reconstruction performance. Under
certain theoretical requirements on the quality of information exchange over
network and RIP parameters of sensor nodes, we show that the DIPP algorithm
converges to a performance level that depends on a scaled additive measurement
noise power (convergence in theory) where the scaling coefficient is a function
of RIP parameters and information processing quality parameters. Using
simulations, we show practical reconstruction performance of DIPP vis-a-vis
amount of undersampling, signal-to-measurement-noise ratios and
network-connectivity conditions.
