Optimized distributed 2D transforms for irregularly sampled sensor network grids using wavelet lifting

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.