Wavelets and differential-dilation equations

Author

Cooklev, Todor ; Berbecel, Gheorghe I. ; Venetsanopoulos, A.N.

Author_Institution

Aware Inc., Lafayette, CA, USA

Volume

48

Issue

8

fYear

2000

fDate

8/1/2000 12:00:00 AM

Firstpage

2258

Lastpage

2268

Abstract

It is shown how differential-dilation equations can be constructed using iterations, similar to the iterations with which wavelets and dilation equations are constructed. A continuous-time wavelet is constructed starting from a differential-dilation equation. It has compact support and excellent time domain and frequency domain localization properties. The wavelet is infinitely differentiable and therefore cannot be obtained using digital filter banks. In addition, the wavelet has excellent approximation properties. New sampling and differentiation techniques are also introduced. Results on image interpolation using the solution of the differential-dilation equation are presented. Examples are given, demonstrating the suitability of the new wavelet function for signal analysis

Keywords

difference equations; image processing; interpolation; iterative methods; wavelet transforms; approximation properties; continuous-time wavelet; differential-dilation equations; differentiation techniques; frequency domain localization; image interpolation; iterations; sampling techniques; signal analysis; time domain localization; wavelet function; Continuous wavelet transforms; Differential equations; Digital filters; Discrete wavelet transforms; Filter bank; Frequency; Interpolation; Signal processing; Wavelet analysis; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.852007

Filename

852007