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Realization of discrete (inverse) wavelet transforms in arbitrary dimensions
Author(s) -
Vogt Frank,
Booksh Karl S.
Publication year - 2005
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.958
Subject(s) - curse of dimensionality , realization (probability) , inverse , chemometrics , computer science , algorithm , wavelet , order (exchange) , mathematics , artificial intelligence , statistics , machine learning , geometry , finance , economics
One‐dimensional (1D) wavelet transforms (WTs) have become a valuable tool in chemometrics, which is currently expanded to multi‐dimensional WTs for applications in multi‐way analyses. In this short communication we present a unified concept for realizing multi‐dimensional WTs of arbitrary order. Goal of this technical report is to demonstrate that multi‐dimensional WTs can be realized solely by means of well‐established 1D WTs. The high practicality of the proposed approach is due to a recursive algorithm, which derives a N ‐dimensional WT ( N ≥ 2) by combining the already available ( N − 1)‐dimensional WT with an additional 1D WT. This concept for designing WTs in arbitrary dimensionality has the potential to open new chemometric perspectives for hyphenated measurement techniques. Copyright © 2006 John Wiley & Sons, Ltd.