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Distributed wavelet processing within sensor networks holds promise for reducing communication energy and wireless bandwidth usage at sensor nodes. Local collaboration among nodes de-correlates measurements, yielding a sparser data set with significant values at far fewer nodes. Sparsity can then be leveraged for subsequent processing such as measurement compression, de-noising, and query routing. A number of factors complicate realizing such a transform in real-world deployments, including irregular spatial placement of nodes and a potentially prohibitive energy cost associated with calculating the transform in-network. In this paper, we address these concerns head-on; our contributions are fourfold. First, we propose a simple interpolatory wavelet transform for irregular sampling grids. Second, using ns-2 simulations of network traffic generated by the transform, we establish for a variety of network configurations break-even points in network size beyond which multiscale data processing provides energy savings. Distributed lossy compression of network measurements provides a representative application for this study. Third, we develop a new protocol for extracting approximations given only a vague notion of source statistics and analyze its energy savings over a more intuitive but naïve approach. Finally, we extend the 2-dimensional (2-D) spatial irregular grid transform to a 3-D spatio-temporal transform, demonstrating the substantial gain of distributed 3-D compression over repeated 2-D compression.

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