Inmathematics andnumerical analysis, theRicker wavelet,^[1]Mexican hat wavelet, orMarr wavelet (forDavid Marr)^[2][3]

${\displaystyle \psi (t)=\frac{2}{\sqrt{3\sigma }{\pi }^{1/4}}\left(1-{\left(\frac{t}{\sigma }\right)}^2\right)e^{-\frac{t^2}{2{\sigma }^2}}}$

is the negativenormalized secondderivative of aGaussian function, i.e., up to scale and normalization, the secondHermite function. It is a special case of the family ofcontinuous wavelets (wavelets used in acontinuous wavelet transform) known asHermitian wavelets. The Ricker wavelet is frequently employed to model seismic data and as a broad-spectrum source term in computational electrodynamics.

${\displaystyle \psi (x,y)=\frac{1}{\pi {\sigma }^4}\left(1-\frac{1}{2}\left(\frac{x^2+y^2}{{\sigma }^2}\right)\right)e^{-\frac{x^2+y^2}{2{\sigma }^2}}}$

The multidimensional generalization of this wavelet is called theLaplacian of Gaussian function. In practice, this wavelet is sometimes approximated by thedifference of Gaussians (DoG) function, because the DoG is separable.^[4] It can therefore save considerable computation time in two or more dimensions.^{[citation needed][dubious –discuss]} The scale-normalized Laplacian (in${\displaystyle L_1}$-norm) is frequently used as ablob detector and for automatic scale selection incomputer vision applications; seeLaplacian of Gaussian andscale space. The relation between this Laplacian of the Gaussian operator and thedifference-of-Gaussians operator is explained in appendix A in Lindeberg (2015).^[5]Derivatives ofcardinal B-splines can also approximate the Mexican hat wavelet.^[6]

• Morlet wavelet

• Continuous wavelets

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