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   -> Volume 4, Issue 8


Preprint: WavBox Software and Related Papers.
 
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taswell@wavbox.com (Carl Taswell)
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PostPosted: Tue Dec 03, 2002 1:30 pm    
Subject: Preprint: WavBox Software and Related Papers.
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Preprint: WavBox Software and Related Papers.

WavBox Software and Related Papers.

The following manuscript has been submitted for publication; it
is available from the author.

Satisficing Search Algorithms for Selecting Near-Best Bases
in Adaptive Tree-Structured Wavelet Transforms

Satisficing search algorithms have been proposed for adaptively
selecting near-best basis 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. Thus,
the algorithms are applicable to 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 are as
good as bottom-up tree search algorithms with additive costs that yield
best bases. 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.

The following abstract has been submitted for presentation at the
1995 MATLAB Conference to be held October 16-18 in Cambridge, MA;
further information about WavBox software is available from the author.

WavBox 4.2 -- A Software Toolbox for Wavelet Transforms and Adaptive
Wavelet Packet Decompositions with New Satisficing Search Algorithms

WavBox provides both a function library and a computing environment for
wavelet transforms and adaptive wavelet packet decompositions. WavBox
contains a collection of these transforms, decompositions, and related
functions that perform multiresolution analyses of 1-D multichannel
signals and 2-D images. The older version 4.1 includes overscaled
pyramid transforms, discrete wavelet transforms, and adaptive wavelet
and cosine packet decompositions by best basis and matching pursuit as
described by Mallat, Coifman, Wickerhauser, and other authors, as well
as Donoho and Johnstone's wavelet shrinkage denoising methods. The new
version 4.2 also implements Taswell's satisficing search algorithms for
the selection of near-best basis decompositions with either additive or
non-additive information costs. Various choices of filter classes
(orthogonal, biorthogonal, etc), filter families (Daubechies, Vetterli,
etc), and convolution versions (interval, circular, extended, etc) exist
for each transform and decomposition. The software has been designed for
efficient automated computation, interactive exploratory data analysis,
and pedagogy. Essential features of the design include: perfect
reconstruction for multiresolution decomposition of data of arbitrary
size not restricted to powers of 2; both command line and graphical user
interfaces with a comprehensive set of plots and visual displays; an object
property expert system with artificial intelligence for configuring valid
property combinations; heirarchical modules and switch-driven function
suites; vector-filter and matrix-operator implementations of convolutions;
extensibility for the inclusion of other wavelet filters, convolution
versions, and transforms; optional arguments with built-in defaults for
most m-files; and extensive on-line help and self-running tutorial demos.

Carl Taswell is the author of both WavBox software and the above related
papers.
He can be reached at "taswell@sccm.stanford.edu" or at "taswell@wavbox.com".
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