An orthogonal multiresolution approximation defines an orthogonal projector on each of the resolution spaces. In the biorthogonal case, the decomposition
defines a (non necessarily orthogonal) projector on V0, and, after rescaling, a projector on each resolution Vj. The projection of a signal f is:
This projection is an approximation of f under the following conditions:
The sufficient condition can be interpreted as follows: the projection on Vj is able to "catch" Taylor expansions of f up to degree p at intervals of length 2j.
The general Stang and Fix conditions are available with proof (PDF v.3, 107 K).
The definition of multiresolution approximations specifies
Is this compatible with the previous theorem? (Answer)