A Biorthogonal wavelet is a wavelet where the associated wavelet transform is invertible but not necessarily orthogonal. Designing biorthogonal wavelets allows more degrees of freedom than orthogonal wavelets. One additional degree of freedom is the possibility to construct symmetric wavelet functions.
\phi,\tilde\phi
\psi,\tilde\psi
a,\tildea
\sumn\in\Zan\tildean+2m=2 ⋅ \deltam,0
n | |
b | |
n=(-1) |
\tildeaM-1-n (n=0,...,N-1)
\tilde
n | |
b | |
n=(-1) |
aM-1-n (n=0,...,N-1)