Efficient data-gathering using graph-based transform and compressed sensing for irregularly positioned sensors

In this work, we propose a decentralized approach for energy efficient data-gathering in a realistic scenario. We address a major limitation of compressed sensing (CS) approaches proposed to data for wireless sensor network (WSN), namely, that they work only on a regular grid tightly coupled to the sparsity basis. Instead, we assume that sensors are irregularly positioned in the field and do not assume that sparsifying basis is known a priori. Under the assumption that the sensor data is smooth in space, we propose to use a graph-based transform (GBT) to sparsify the sensor data measured at randomly positioned sensors. We first represent the random topology as a graph then construct the GBT as a sparsifying basis. With the GBT, we propose a heuristic design of the data-gathering where aggregations happen at the sensors with fewer neighbors in the graph. In our simulations, our proposed approach shows better performance in terms of total power consumption for a given reconstruction MSE, as compared to other CS approaches proposed for WSN.