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 potenti al solution, Compressed Sensing (CS) has been proposed, becau se it requires capturing a smaller number of samples for succes sful 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 new distributed measurement syste m that constructs measurements within spatially-localizedclusters. We first introduce the concept of maximum energy overlap between clusters and basis functions ( β), and show thatβ can be used to estimate the minimum number of measurements require d for accurate reconstruction. Based on this metric, we propo se a centralized iterative algorithm for joint optimization o f the energy overlap and distance between sensors in each cluster . Our simulation results show that we can achieve significant savi ngs in transport cost with small reconstruction error.

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