Family of continuous wavelets
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, for each positive :[1]
where
denotes the
probabilist's Hermite polynomial.
The normalization coefficient is given by,
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.
Examples
The first three derivatives of the Gaussian function with :
are:
and their
norms
.
Normalizing the derivatives yields three Hermitian wavelets:
See also
References
External links