History of Mathematics Special Interest Group of the Mathematical Association of America (HOMSIGMAA) On the Foundations of X-Ray Computed Tomography in Medicine: A Fundamental Review of the ‘Radon transform’ and a Tribute to

Objective: To acknowledge the work and life of the Austrian mathematician Johann Radon, motivated by a historical narrative on the development of the computed tomography scanner. Methods: Information was obtained from journal articles, textbooks, the Nobel web site, and proceedings from mathematical symposiums. Results: The computed tomography scanner changed the paradigm of medical imaging. This was a direct result of collaboration between Godfrey Hounsfield and James Ambrose in the 1970s. However, the theoretical basis of computed tomography had been published by Allan Cormack a decade earlier, and a generalized solution to the problem had been described by Johann Radon in 1917 (i.e., the ‘Radon transform’). Subsequently, both Hounsfield and Cormack were recipients of the 1979 Nobel Prize in Physiology or Medicine for their achievements in computed tomography imaging. Conclusions: An appreciation of the Radon transform serves as a prerequisite to gain deeper insight into signal processing in computed tomography. Such insight offers opportunities to advance optimization strategies in health physics relative to computed tomography quality assurance protocols. Advances in Knowledge: As we close in on the 100 year anniversary of the publication of the Radon transform, a review of the literature reveals that a wide-ranging treatise on Johann Radon is not available. This paper attempts to correct that oversight.