Wavelet-based distributed data processing holds much promise for sensor networks; however, irregular sensor node placement precludes the direct application of standard wavelet techniques. In this paper, we develop a new distributed wavelet transform based on lifting that takes into account irregular sampling and provides a piecewise-planar multiresolution representation of the sensed data. We develop the transform theory; outline how to implement it in a multi-hop, wireless sensor network; and illustrate with several simulations. The new transform performs on par with conventional wavelet methods in a head-to-head comparison on a regular grid of sensor nodes.

We outline a distributed coding technique for images captured from sensors with overlapping fields of view in a sensor network. First, images from correlated views are roughly registered (relative to a sensor of primary interest) via a low-bandwidth data-sharing method involving image feahlre points and feature point wrrespondence. An area of overlap is then idenuied, and each sensor transmits a low-resolution version of the common image block to the receiver, amortizing the coding wst for that block among the set of sensors. Super-resolution techniques are finally employed at the receiver to recmstruct a high-resolution version of the common block.We discuss the registration and super-resolution techniques used and present examples of each step in the proposed coding process. A numerical analysis illustrating the potential coding benefit follows, and we conclude with a brief discussion of the key issues remaining to be resolved on the path to coder robustness.

Abstract-Wireless sensor networks provide a natural application area for distributed data processing algorithms. Power consumption for communication between sensor network nodes typically dominates over that for local data processing, so it is often more efficient to process data in the network than it is to send data to a remote, central collection point for analysis. Distributed wavelet analysis represents one such technique, whereby local collaboration among nodes de-correlates measurements, yielding a sparser data set with fewer significant values. This sparsity can then be leveraged to suppress errors in nodes' measurements, which are typically gathered by inexpensive sensors subject to measurement noise. In this paper, we briefly review the details of a distributed wavelet processing protocol for sensor networks based on the theory of lifting, and we develop a suite of wavelet de-noising protocols for distributed de-noising of measurements. We illustrate the effectiveness of the system with a series of numeric examples.

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