Hermitian wavelet
Family of continuous wavelets / From Wikipedia, the free encyclopedia
Hermitian wavelets are a family of discrete and continuous wavelets used in the continuous and discrete Hermite wavelet transform. The Hermitian wavelet is defined as the derivative of a Gaussian distribution for each positive :[1]where in this case the (probabilist) Hermite polynomial can be considered.
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The normalization coefficient is given byThe function is said to be an admissible Hermite wavelet if it satisfies the admissibility relation:[2]
where is the Hermite transform of .
The perfector in the resolution of the identity of the continuous wavelet transform for this wavelet is given by the formula[further explanation needed]In computer vision and image processing, Gaussian derivative operators of different orders are frequently used as a basis for expressing various types of visual operations; see scale space and N-jet.[3]