The wide designed discrete wavelet transforms based on the perfect translation invariance theorem

Author

Toda, Hiroshi ; Zhang, Zhong ; Imamura, Takashi

Author_Institution

Dept. of Production Syst. Eng., Toyohashi Univ. of Technol., Toyohashi, Japan

fYear

2011

fDate

10-13 July 2011

Firstpage

260

Lastpage

265

Abstract

The perfect translation invariance theorem has already been proven, which gives the condition of the perfect translation invariance for complex discrete wavelet transforms of an arbitrary square integrable function. In this paper, three types of discrete wavelet transforms based on this theorem are introduced. One of them is designed with variable density of complex wavelets in the time and frequency domains, and another of them is designed with customizable complex wavelets, and the other is designed as a real-valued discrete wavelet transform having perfect translation invariance.

Keywords

discrete wavelet transforms; time-frequency analysis; arbitrary square integrable function; complex discrete wavelet transform; customizable complex wavelet; frequency domains; perfect translation invariance theorem; real-valued discrete wavelet transform; time domains; wide designed discrete wavelet transform; Image reconstruction; Transforms; Complex Discrete Wavelet Transform; Customizable Complex Discrete Wavelet Transform; Perfect Translation Invariance; Shift Invariance;

fLanguage

English

Publisher

ieee

Conference_Titel

Wavelet Analysis and Pattern Recognition (ICWAPR), 2011 International Conference on

Conference_Location

Guilin

ISSN

2158-5695

Print_ISBN

978-1-4577-0283-9

Type

conf

DOI

10.1109/ICWAPR.2011.6014503

Filename

6014503