Lemarié's Wavelet
A wavelet used in multiresolution representation to analyze the information content of images. The wavelet is defined by
![画像: H(omega)=[2(1-u)^4(315-420u+126u^2-4u^3)/(315-420v+126v^2-4v^3)]^(1/2),](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/LemariesWavelet/NumberedEquation1.svg){kind=link}
where
u = sin^2(1/2omega)
(2)
v = sin^2omega
(3)
(Mallat 1989ab).
See also
WaveletExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Mallat, S. G. "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation." IEEE Trans. Pattern Analysis Machine Intel. 11, 674-693, 1989a.Mallat, S. G. "Multiresolution Approximation and Wavelet Orthonormal Bases of L^2(R)." Trans. Amer. Math. Soc. 315, 69-87, 1989b.Referenced on Wolfram|Alpha
Lemarié's WaveletCite this as:
Weisstein, Eric W. "Lemarié's Wavelet." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LemariesWavelet.html