Hermitian wavelets are a family of continuous wavelets, used in the continuous wavelet transform

Continuous wavelet transform

A continuous wavelet transform is used to divide a continuous-time function into wavelets. Unlike Fourier transform, the continuous wavelet transform possesses the ability to construct a time-frequency representation of a signal that offers very good time and frequency localization...

. The Hermitian wavelet is defined as the derivative of a Gaussian:



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

Computer vision

Computer vision is a field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions...

 and image processing

Image processing

In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...

, 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

N-jet

An N-jet is the set of derivatives of a function f up to order N.Specifically, in the area of computer vision, the N-jet is usually computed from a scale-space representation L of the input image f, and the partial derivatives of L are used as a basis for expressing various types of visual modules...

.

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: