Consider a wireless sensor network with N sensor nodes measuring data which are correlated temporally or spatially. We consider the problem of reconstructing the original data by only transmitting M N sensor readings while guaranteeing that the reconstruction error is small. Assuming the original signal is "smooth" with respect to the network topology, our approach to gather measurements from a random subset of nodes and then interpolate with respect to the graph Laplacian eigenbasis,

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... ideas from compressed sensing. We propose algorithms for both temporally and spatially correlated signals, and the performance of these algorithms is verified using both synthesized data and real world data. Significant savings are made in terms of energy resources, bandwidth, and query latency.