Joint Optimization of Transport Cost and Reconstruction for Spatially-Localized Compressed Sensing in Multi-Hop Sensor Networks

In sensor networks, energy efficient data manipulation / transmission is very important for data gathering, due to significant power constraints on the sensors. As a potential solution, Compressed Sensing (CS) has been proposed, because it requires capturing a smaller number of samples for successful reconstruction of sparse data. Traditional CS does not take explicitly into consideration the cost of each measurement (it simply tries to minimize the number of measurements), and this ignores the need to transport measurements over the sensor network. In this paper, we study CS approaches for sensor networks that are spatially-localized, thus reducing the cost of data gathering. In particular, we study the reconstruction accuracy properties of a spatially-localized distributed CS system. We introduce the concept of maximum energy overlap between clusters and basis functions, and show that the corresponding metric can be used to estimate the minimum number of measurements needed to achieve accurate reconstruction. Based on this metric, we propose a centralized iterative algorithm for joint optimization of the energy overlap and distance between nodes in each cluster. Our simulation results show that we can achieve significant savings in transport cost with small reconstruction error.