Calderón's Formula

$$f(x)=C_\psi \int_{-\infty}^\infty \int_{-\infty}^\infty \left\langle{f,\psi^{a,b}}\right\rangle{}\psi^{a,b}(x)a^{-2}\,da\,db,$$

where

$$\psi^{a,b}(x)=\vert a\vert^{-1/2}\psi\left({x-b\over a}\right).$$

This result was originally derived using Harmonic Analysis, but also follows from a Wavelets viewpoint.