Hermitian wavelet

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Hermitian wavelets are a family of continuous wavelets, used in the continuous wavelet transform. The Hermitian wavelet is defined as the derivative of a Gaussian distribution:

where denotes the Hermite polynomial.

The normalisation coefficient is given by:

The prefactor in the resolution of the identity of the continuous wavelet transform for this wavelet is given by:

i.e. Hermitian wavelets are admissible for all positive .

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.

Examples of Hermitian wavelets: Starting from a Gaussian function with :

the first 3 derivatives read

and their norms

So the wavelets which are the negative normalized derivatives are: