Combining the Radon, Markov, and Stieltjes Transforms for Object Reconstruction

In shape reconstruction, the celebrated Fourier slice theorem plays an essential role. By virtue of the relation between the Radon transform, the Fourier transform and the 2-dimensional inverse Fourier transform, the shape of an object can be reconstructed from the knowledge of the object’s Radon transform. Unfortunately, a discrete implementation requires the use of interpolation techniques, such as in the filtered back projection.