Title :
Simple wavelet frames for finite functions on discrete tori
Author :
Sarty, Gordon E.
Author_Institution :
Dept. of Med. Imaging, Saskatchewan Univ., Saskatoon, Sask., Canada
fDate :
2/1/2000 12:00:00 AM
Abstract :
A new approach to numerical wavelet transforms is described where sampled n-dimensional signal data are treated as finite functions on discrete tori Tn. This approach shows that the undecimated numerical wavelet transform leads to decomposition onto a frame in the space of square-summable functions on the discrete torus l2 (Tn)
Keywords :
discrete wavelet transforms; filtering theory; functional analysis; group theory; image processing; signal sampling; 1D signal; 2D image processing; affine group; discrete tori wavelet transform; finite functions; numerical wavelet transforms; sampled n-dimensional signal data; signal processing; square-summable functions; undecimated numerical wavelet transform; wavelet filter; wavelet frames; Continuous wavelet transforms; Discrete Fourier transforms; Discrete wavelet transforms; Fourier transforms; Integral equations; Multiresolution analysis; Signal processing; Wavelet analysis; Wavelet domain; Wavelet transforms;
Journal_Title :
Signal Processing, IEEE Transactions on
