Distributed Compressed Sensing for Sensor Networks with Packet Erasures

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.