Biorthogonal wavelets are defined similarly to orthogonal wavelets, except that the starting point is biorthogonal multiresolution approximations. The following decompositions are performed:
Like in the orthogonal case, a signal in L2 can be written as
Below is a biorthogonal system which includes a cubic B-spline. Dropping the orthogonality constraint makes possible to have both regularity and symmetry.
The construction of biorthogonal wavelets over the interval or in dimension 2 will not be presented here. It follows the same lines as in the orthogonal case.