Ludwig's Inversion Formula

Expresses a function in terms of its Radon Transform,

$$f(x,y) = {\mathcal R}^{-1}({\mathcal R} f)(x, y)$$

$$= {1\over\pi}{1\over 2\pi}\int_{-\infty}^\infty{{\partial\over\partial p}({\mathcal R}f)(p,\alpha)\over x\cos\alpha+y\sin\alpha-p}\,dp\,d\alpha.$$

See also Radon Transform