text: Fourier-domain reconstruction algorithm Reconstruction can be made using interpolation. Assume  projections of  are generated at equally spaced angles, each sampled at the same rate. The discrete Fourier transform (DFT) on each projection yields sampling in the frequency domain. Combining all the frequency-sampled projections generates a polar raster in the frequency domain. The polar raster is sparse, so interpolation is used to fill the unknown DFT points, and reconstruction can be done through the inverse discrete Fourier transform. Reconstruction performance may improve by designing methods to change the sparsity of the polar raster, facilitating the effectiveness of interpolation.
  For instance, a concentric square raster in the frequency domain can be obtained by changing the angle between each projection as follow:
  where  is highest frequency to be evaluated.
  The concentric square raster improves computational efficiency by allowing all the interpolation positions to be on rectangular DFT lattice. Furthermore, it reduces the interpolation error. Yet, the Fourier-Transform algorithm has a disadvantage of producing inherently noisy output.
  Back projection algorithm
  In practice of tomographic image reconstruction, often a stabilized and discretized version of the inverse Radon transform is used, known as the filtered back projection algorithm.
  With a sampled discrete system, the inverse Radon transform is
  where  is the angular spacing between the projections and  is a Radon kernel with frequency response .