Distributed Multiscale Data Analysis and Processing for Sensor Networks

While multiresolution data analysis, processing, and compression hold considerable promise for sensor network applications, progress has been confounded by two factors. First, typical sensor data are irregularly spaced, which is incompatible with standard wavelet techniques. Second, the communication overhead of multiscale algorithms can become prohibitive. In this paper, we take a first step in addressing both shortcomings by introducing two new distributed multiresolution transforms. Our irregularly sampled Haar wavelet pyramid and telescoping Haar orthonormal wavelet basis provide efficient piecewise-constant approximations of sensor data. We illustrate with examples from distributed data compression and in-network wavelet de-noising.