Wavelet packet representations from local maxima in their expansion coefficients

Graham H. Watson

doi:10.1117/12.205420

6 April 1995 Wavelet packet representations from local maxima in their expansion coefficients

Graham H. Watson

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205420
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

A new method of adaptive waveform analysis, called shape adaptive wavelet analysis, is presented where the basis vectors (wavelet packets) are initially considered as functions of continuous variables, in particular position/time, frequency, and scale. A discrete subset of these wavelet packets is chosen from local maxima of the modulus of their expansion coefficients, in general resulting in a non-orthogonal basis. Redundancy removal, when required, is implemented using an algorithm loosely based on Gram-Schmidt orthogonalization, where basis vectors are chosen to maximize the modulus of the projection of the residual perpendicular to the space spanned by the basis vectors chosen previously, thus maximizing `information content.' In cases where this representation is not sufficiently accurate an additional process of feature substraction is available enabling representations of arbitrary accuracy. It is shown, however, that there are sometimes advantages in retaining redundancy in the wavelet packet characterization of the signal, in particular where noise is present. The method presented in this paper is compared with the wavelet packet transform of Coifman et al. and with the matching pursuit algorithm of Mallat et al., and is shown to provide an improved characterization under circumstances which are of relevance in surveillance, detection, and classification in noisy or cluttered backgrounds. The method is shown to be well suited to characterizations in higher-dimensional wavelet packet spaces, where additional shape parameters, for example chirp angle, characterize the wavelet packets in addition to position, frequency, and scale.

Citation Download Citation

Graham H. Watson "Wavelet packet representations from local maxima in their expansion coefficients", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205420

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
12 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Wavelets

Associative arrays

Image filtering

Signal detection

Electronic filtering

Shape analysis

Wavelet transforms

Show All Keywords

Keywords/Phrases

Search In:

Publication Years