Distributed Field Reconstruction in Wireless Sensor Networks Based on Hybrid Shift-Invariant Spaces

We use the theory and algorithms developed for so-called shift-invariant spaces to develop a novel distributed architecture for sampling and reconstructing time-varying non-bandlimited physical fields in wireless sensor networks. We introduce hybrid shift-invariant spaces that generalize conventional shift-invariant spaces and can adapt to local smoothness properties of the field. Using shift-invariant spaces with compactly supported generator functions allows us to split the global reconstruction into several smaller local problems that can be solved independently. Capitalizing on the sparsity of the matrices involved in the reconstruction, we propose direct and iterative reconstruction algorithms whose complexity per time slot scales only linearly with the number of sensor nodes. We furthermore analyze the impact of sensor localization errors on the mean square error of the reconstructed field. Numerical simulations illustrate that the proposed field reconstruction scheme performs close to bandlimited reconstruction and is less sensitive to sensor location errors while providing a significant reduction in computational complexity.