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WavBox 4: A Software Toolbox for Wavelet Transforms and Adaptive Wavelet Packet Decompositions

  • Carl Taswell
Part of the Lecture Notes in Statistics book series (LNS, volume 103)

Abstract

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 current version 4.1c includes overscaled pyramid transforms, discrete wavelet transforms, and adaptive wavelet and cosine packet decompositions by best level, best basis, and matching pursuit as described by Mallat, Coifman, Wickerhauser, and other authors. WavBox also implements Taswell’s new search algorithms with decision criteria, called near-best basis and non-additive information costs respectively, for selecting bases in wavelet packet transforms, as well as Donoho and Johnstone’s wavelet shrinkage denoising methods. 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.

Keywords

Discrete Wavelet Transform Wavelet Packet Multiresolution Analysis Matching Pursuit Wavelet Packet Transform 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    The Math Works, Inc., Natick, MA. MATLAB Reference Guide, August 1992.Google Scholar
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    Carl Taswell. MATLAB wavelet toolbox. Wavelet Digest, 2(11), July 1993. Topic #7.Google Scholar
  3. [3]
    Carl Taswell. Top-down and bottom-up tree search algorithms for selecting bases in wavelet packet transforms. In Anestis Antoniadis and Georges Oppenheim, editors, Wavelets and Statistics, Lecture notes in Statistics, pages 345–360 Springer Verlag, 1995. Proceedings of the Villard de Lans Conference November 1994.Google Scholar
  4. [4]
    Carl Taswell and Kevin C. McGill. Wavelet transform algorithms for finite-duration discrete- time signals: Signal-end effects. Technical Report NA-91-07, Computer Science Department, Stanford University, Stanford, CA, November 1991.Google Scholar
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    Carl Taswell and Kevin C. McGill. Algorithm 735: Wavelet transform algorithms for finite- duration discrete-time signals. ACM Transactions on Mathematical Software, 20 (3): 398 – 412, September 1994.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York 1995

Authors and Affiliations

  • Carl Taswell
    • 1
  1. 1.Scientific Computing and Computational MathematicsStanford UniversityStanfordUSA

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