Hermitian wavelet
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:
