Top-Down and Bottom-Up Tree Search Algorithms for Selecting Bases in Wavelet Packet Transforms
Search algorithms for finding signal decompositions called near-best bases using decision criteria called non-additive information costs have recently been proposed by Taswell  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 . All wavelet packet basis decompositions are also compared with the nonorthogonal matching pursuit decomposition of Mallat and Zhang  and the orthogonal matching pursuit decomposition of Patiet al . 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.
KeywordsShannon Entropy Wavelet Packet Good Basis Match Pursuit Orthogonal Match Pursuit
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