Entropy-based algorithms for best basis selection
Coifman, R.R.
Wickerhauser, M.V.
Dept. of Math., Yale Univ., New Haven, CT;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Mar 1992
Volume: 38,
Issue: 2, Part 2
On page(s): 713-718
ISSN: 0018-9448
References Cited: 8
CODEN: IETTAW
INSPEC Accession Number: 4196023
Digital Object Identifier: 10.1109/18.119732
Current Version Published: 2002-08-06
Abstract
Adapted waveform analysis uses a library of orthonormal bases and
an efficiency functional to match a basis to a given signal or family of
signals. It permits efficient compression of a variety of signals, such
as sound and images. The predefined libraries of modulated waveforms
include orthogonal wavelet-packets and localized trigonometric
functions, and have reasonably well-controlled time-frequency
localization properties. The idea is to build out of the library
functions an orthonormal basis relative to which the given signal or
collection of signals has the lowest information cost. The method relies
heavily on the remarkable orthogonality properties of the new libraries:
all expansions in a given library conserve energy and are thus
comparable. Several cost functionals are useful; one of the most
attractive is Shannon entropy, which has a geometric interpretation in
this context
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