An architecture for distributed wavelet analysis and processing in sensor networks

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.