Fast discrete W transforms via computation of moments

Author

Liu, J.G. ; Liu, Y.Z. ; Wang, G.Y.

Author_Institution

Inst. for Pattern Recognition & Artificial Intelligence, Huazhong Univ. of Sci. & Technol., Wuhan, China

Volume

53

Issue

2

fYear

2005

fDate

2/1/2005 12:00:00 AM

Firstpage

654

Lastpage

659

Abstract

A novel approach to compute all four types of Discrete W transform (DWT) is proposed. By using kernel transforms and Taylor expansions, a DWT is approximated by a linear sum of discrete moments. This enables us to use computational techniques developed for computing moments to compute DWTs efficiently. The amount of multiplications used in our method is O(Nlog₂N/log₂log₂N) and is superior to the O(Nlog₂N) in the conventional DWT. The proposed algorithm achieves a simple computational structure and naturally deals with any sequence lengths.

Keywords

computational complexity; discrete wavelet transforms; method of moments; signal processing; digital signal processing; fast discrete W transform; kernel transform; moment computation; Artificial intelligence; Computer vision; Discrete Fourier transforms; Discrete transforms; Discrete wavelet transforms; Kernel; Linear approximation; Pattern recognition; Signal processing algorithms; Taylor series; Discrete W transforms; fast transformation; moment;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2004.840716

Filename

1381756