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Lemarié's Wavelet

A wavelet used in multiresolution representation to analyze the information content of images. The Wavelet is defined by

H(\omega)=\left[{2(1-u)^4{315-420u+126u^2-4u^3\over 315-420v+126v^2-4v^3}}\right]^{1/2},

$\displaystyle u$ $\textstyle \equiv$ $\displaystyle \sin^2({\textstyle{1\over 2}}\omega)$  
$\displaystyle v$ $\textstyle \equiv$ $\displaystyle \sin^2\omega$  

(Mallat 1989).

See also Wavelet


Mallat, S. G. ``A Theory for Multiresolution Signal Decomposition: The Wavelet Representation.'' IEEE Trans. Pattern Analysis Machine Intel. 11, 674-693, 1989.

Mallat, S. G. ``Multiresolution Approximation and Wavelet Orthonormal Bases of $L^2(\Bbb{R})$.'' Trans. Amer. Math. Soc. 315, 69-87, 1989.

© 1996-9 Eric W. Weisstein