One of the most important mathematical problems in the last 25 years has been the problem of reconstructing images from its projections. In medical imaging this is referred as computerized tomography and it involves the reconstruction of a function f from the line integrals of f. This is vital to the medical community because it allows for non-invasive examination of the interior of the human body. In this thesis we discuss how human data from a CT scan can be represented by the Radon transform and how, with certain numerical techniques, we can recover internal images of the human body. A popular method is Filtered Backprojection which uses Fourier transforms to invert the Radon transform and reconstruct medial images.
