Top-Down and Bottom-Up Tree Search Algorithms for Selecting Bases in Wavelet Packet Transforms

Abstract

Search algorithms for finding signal decompositions called near-best bases using decision criteria called non-additive information costs have recently been proposed by Taswell [12] for selecting bases in wavelet packet transforms represented as binary trees. These methods are extended here to distinguish between top-down and bottom-up tree searches. Other new non-additive information cost functions are also proposed. In particular, the near-best basis with the non-additive cost of the Shannon entropy on probabilities is compared against the best basis with the additive cost of the Coifman-Wickerhauser entropy on energies [3]. All wavelet packet basis decompositions are also compared with the nonorthogonal matching pursuit decomposition of Mallat and Zhang [7] and the orthogonal matching pursuit decomposition of Patiet al [8]. Monte Carlo experiments using a constant-bit-rate variable-distortion paradigm for lossy compression suggest that the statistical performance of top-down near-best bases with non-additive costs is superior to that of bottom-up best bases with additive costs. Top-down near-best bases provide a significant increase in computational efficiency with reductions in memory, flops, and time while nevertheless maintaining similar coding efficiency with comparable re-construction errors measured by ℓ^p-norms. Finally, a new compression scheme called parameterized model coding is introduced and demonstrated with results showing better compression than standard scalar quantization coding at comparable levels of distortion.