  We study two approaches to distributed compressed sensing for in-network data
compression and signal reconstruction at a sink in a wireless sensor network
where sensors are placed on a straight line. Communication to the sink is
considered to be bandwidth-constrained due to the large number of devices. By
using distributed compressed sensing for compression of the data in the
network, the communication cost (bandwith usage) to the sink can be decreased
at the expense of delay induced by the local communication necessary for
compression. We investigate the relation between cost and delay given a certain
reconstruction performance requirement when using basis pursuit denoising for
reconstruction. Moreover, we analyze and compare the performance degradation
due to erased packets sent to the sink of the two approaches.
