then states: where

Thus the two-dimensional Fourier transform of the initial function along a line at the inclination angle is the one variable Fourier transform of the Radon transform (acquired at angle ) of that function. This fact can be used to compute both the Radon transform and its inverse. The result can be generalized into n dimensions:

Range characterization

The image of the Radon transform on can be characterized for functions of sufficient regularity and decay. Since the same unoriented hyperplane is

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