text: So the equation above can be rewritten as
  where  represents  and  is the Dirac delta function. This function is known as the Radon transform (or sinogram) of the 2D object.
  The Fourier Transform of the projection can be written as
  where
  represents a slice of the 2D Fourier transform of  at angle . Using the inverse Fourier transform, the inverse Radon transform formula can be easily derived.
  where  is the derivative of the Hilbert transform of
  In theory, the inverse Radon transformation would yield the original image. The projection-slice theorem tells us that if we had an infinite number of one-dimensional projections of an object taken at an infinite number of angles, we could perfectly reconstruct the original object, . However, there will only be a finite number of projections available in practice.
  Assuming  has effective diameter  and desired resolution is , a rule of thumb for the number of projections needed for reconstruction is
  Reconstruction algorithms
  Practical reconstruction algorithms have been developed to implement the process of reconstruction of a three-dimensional object from its projections. These algorithms are designed largely based on the mathematics of the X-ray transform, statistical knowledge of the data acquisition process and geometry of the data imaging system.