A multiscale data representation for distributed sensor networks

Though several wavelet-based compression solutions for wireless sensor network measurements have been proposed, no such technique has yet appreciated the need to couple a wavelet transform tolerant of irregularly sampled data with the data transport protocol governing communications in the network. As power is at a premium in sensor nodes, such a technique is necessary to reduce costly communication overhead. To this end, we present an irregular wavelet transform capable of adapting to an arbitrary, multiscale network routing hierarchy. Inspired by the Haar wavelet in the regular setting, our wavelet basis forms a tight frame adapted to the structure of the network. We demonstrate results highlighting the approximation capabilities of such a transform and the clear reduction in communication cost when transmitting a compressed snapshot of the network to an outside user.