Biorthogonal wavelet

Summary

A biorthogonal wavelet is a pair of wavelets $\psi$ and $\tilde\psi$ whose dilated and translated copies are dual to each other. It replaces a single wavelet whose copies are orthonormal. One family is used to compute the coefficients of a function and the other to rebuild it. Giving up orthogonality allows wavelets that are both compactly supported and symmetric. Among real orthonormal wavelets, only the Haar wavelet has both properties. Biorthogonal wavelets are used in image compression, for example in the JPEG 2000 standard.