Satisficing search algorithms for selecting near-best bases in adaptive tree-structured wavelet transforms

Satisficing search algorithms are proposed for adaptively selecting near-best basis and near-best frame decompositions in redundant tree-structured wavelet transforms. Any of a variety of additive or non-additive information cost functions can be used as the decision criterion for comparing and selecting nodes when searching through the tree. The algorithms are applicable to tree-structured transforms generated by any kind of wavelet whether orthogonal, biorthogonal, or non-orthogonal. These satisficing search algorithms implement sub-optimizing rather than optimizing principles, and acquire the important advantage of reduced computational complexity with significant savings in memory, flops, and time. Despite the sub-optimal approach, top-down tree-search algorithms with additive or non-additive costs that yield near-best bases can be considered, in certain important and practical situations, better than bottom-up tree-search algorithms with additive costs that yield best bases. Here “better than” means that effectively the same level of performance can be attained for a relative fraction of the computational work. Experimental results comparing the various information cost functions and basis selection methods are demonstrated for both data compression of real speech and time-frequency analysis of artificial transients. Keywords— Satisficing search, near-best basis, information cost, wavelet packet transform, cosine packet transform, timefrequency analysis, data compression, speech coding. EDICS— SP 2.2.1, 2.2.7, 2.4.4, and 2.4.5.