A translation-invariant wavelet representation algorithm with applications

Author

Liang, Jie ; Parks, Thomas W.

Author_Institution

Sch. of Electr. Eng., Cornell Univ., Ithaca, NY, USA

Volume

44

Issue

2

fYear

1996

fDate

2/1/1996 12:00:00 AM

Firstpage

225

Lastpage

232

Abstract

We address the time-varying problem of wavelet transforms, and a new translation-invariant wavelet representation algorithm is proposed. Using the algorithm introduced by Beylkin (see SIAM J. Numer. Anal., vol. 29, p.1716-1740, 1992), we compute the wavelet transform for all the circular time shifts of a length-N signal in O(N log N) operations. The wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function. We apply the translation-invariant representation algorithm to a geoacoustic data compression application. The results show that the new algorithm can reduce the distortion (the squared error in our case) substantially, if the input signals are transients that are sensitive to time shifts

Keywords

acoustic signal processing; data compression; geophysical signal processing; signal representation; transients; tree searching; wavelet transforms; binary tree search algorithm; circular time shifts; cost function; distortion reduction; geoacoustic data compression; input signals; minimal cost; signal representation; squared error; time-varying problem; transients; translation-invariant wavelet representation algorithm; wavelet coefficients; wavelet transform; Binary trees; Cost function; Data compression; Discrete wavelet transforms; Distortion; Filter bank; Reconstruction algorithms; Signal processing algorithms; Wavelet coefficients; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.485919

Filename

485919