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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 . Examples of Hermitian wavelets:Starting from Gaussian function with : the first 3 derivatives read as, and their norms

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  • Hermitian wavelet (en)
  • 厄爾米特小波 (zh)
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  • 埃爾米特小波由埃爾米特多項式組成，第n個埃爾米特小波來自於高斯函數的第n階導數。 物理學上的埃爾米特多項式定義為 可以用遞迴方式得到: 連續小波轉換的母小波可以表示成 ，其中a是膨脹參數，b是位移， a,b∈R且 a≠0 若 ，，則變成具有離散參數的小波轉換: ，其中k,n∈R 埃爾米特小波的母小波定義為 ，包含四個參數，其中k是任意正整數，影響母小波的縮放， 影響母小波的平移位置，m是埃爾米特多項式的階層，其定義在[0,1)，數學式如下: (zh)
  • 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 . Examples of Hermitian wavelets:Starting from Gaussian function with : the first 3 derivatives read as, and their norms (en)
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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 Gaussian function with : the first 3 derivatives read as, and their norms So the wavelets which are the negative normalized derivatives are: (en)
  • 埃爾米特小波由埃爾米特多項式組成，第n個埃爾米特小波來自於高斯函數的第n階導數。 物理學上的埃爾米特多項式定義為 可以用遞迴方式得到: 連續小波轉換的母小波可以表示成 ，其中a是膨脹參數，b是位移， a,b∈R且 a≠0 若 ，，則變成具有離散參數的小波轉換: ，其中k,n∈R 埃爾米特小波的母小波定義為 ，包含四個參數，其中k是任意正整數，影響母小波的縮放， 影響母小波的平移位置，m是埃爾米特多項式的階層，其定義在[0,1)，數學式如下: (zh)
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