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We address the design and optimization of an energy-efficient lifting-based 2D transform for wireless sensor networks with irregular spatial sampling. The 2D transform is designed to allow for unidirectional computation found in existing path-wise transforms, thereby eliminating costly backward transmissions often required by existing 2D transforms, while simultaneously achieving greater data decorrelation than those path-wise transforms. We also propose a framework for optimizing the 2D transform via an extension of standard dynamic programming (DP) algorithms, where a selection is made among alternative coding schemes (e.g., different number of levels in the wavelet decomposition). A recursive DP formulation is provided and an algorithm is given that finds the minimum cost coding scheme assignment for our proposed 2D transform.

A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These transforms can be computed as data is routed towards the collection (or sink) node in the tree and exploit data correlation between nodes in the tree. Moreover, when used in wireless sensor networks, these transforms can also leverage data received at nodes via broadcast wireless communications. Various constructions of unidirectional transforms are also provided for use in data gathering in wireless sensor networks. New wavelet transforms are also proposed which provide significant improvements over existing unidirectional transforms.

Signal compression is an important tool for reducing communication costs and increasing the lifetime of wireless sensor network deployments. In this paper, we overview and classify an array of proposed compression methods, with an emphasis on illustrating the differences between the various approaches.

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