Hermitian_wavelet
Hermitian wavelet
Family of continuous wavelets
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]
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where in this case we consider the (probabilist) Hermite polynomial . The normalization coefficient is given by,
The 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]