The Fourier slice theorem is derived by taking the one-dimensional Fourier transform of a parallel projection and noting that it is equal to a slice of the two-dimensional Fourier transform of the original object. It follows that given the projection data, it should then be possible to estimate the object by simply performing the 2D inverse Fourier transform.

Start by defining the 2D Fourier transform of the object function as:

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http://www.eng.warwick.ac.uk/oel/courses/undergrad/lec13/fourier_slice.htm