Dirac, faraday, born and medical imaging

Most modern medical imaging methods rely on the analysis and processing of acquired data to reconstruct a desired tomographic image, generally via digital methods. A unified view of these techniques is developed here, using classical approaches associated with Dirac, Faraday and Born. A formalism due to Dirac is shown to provide a unifying basis for standard reconstruction- from-projection algorithms, as well as to point the way towards new methods. An unusual approach towards enhancing backprojected images is based on Faraday´s work, while an approximation first proposed by Born is shown to link imaging methods utilising scattered radiation, to those based on a linear ray hypothesis.