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 nonadditive 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 nonorthogonal. These satisficing search algorithms implement suboptimizing rather than optimizing principles, and acquire the important advantage of reduced computational complexity with significant savings in memory, flops, and time. Despite the suboptimal approach, top-down tree-search algorithms with additive or nonadditive 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.