| A wavelet software toolbox called WavBox has been developed for wavelet transforms and adaptive wavelet packet decompositions. WavBox provides both a function library for use in programming and a computing environment for use in interactive exploratory data analysis. The scope of this work therefore encompasses both computational mathematics with the development of new algorithms as well as computer science with the development of new interfaces, both textual command and graphical icon, for the use of these algorithms within an interactive computing environment.;The development of interfaces for the WavBox computing environment focused on principles of convenience and utility for the user. All transform and decomposition algorithms are integrated for simultaneous use with both textual command and graphical icon interfaces through an architectural design incorporating heirarchical modules, switch-driven function suites, and an object property expert system with artificial intelligence for configuring valid property combinations.;The development of computational algorithms focused on principles of pragmatism. New algorithms include the development of (a) methods for computing the wavelet transform of signals of arbitrary length not restricted to a power of two, (b) satisficing searches instead of optimizing searches for selecting bases in wavelet packet transforms, and (c) parameterized-model coding instead of quantized-vector or quantized-scalar coding for further compression of the selected transform decompositions. These methods are shown to be especially useful for image compression.;Wavelet packet basis decompositions require selection of a single basis represented as the terminal leaves of a subtree within a redundant collection of many bases represented as the full tree. For this purpose, top-down and bottom-up tree searches with additive and non-additive information cost functions as decision criteria are proposed as selection methods. These new algorithms are satisficing searches and find near-best basis decompositions.;The satisficing searches are benchmarked in computational experiments comparing their performance with optimizing searches (the Coifman-Wickerhauser best basis decomposition and the Mallat-Zhang matching pursuit decomposition). Near-best basis decompositions outperform the other decompositions as measured by significant increases in efficiency of computation (reductions in memory, flops, and time) for comparable levels of distortion on reconstruction after fixed-rate lossy compression. |
