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 Johann Radon HOMSIGMAA Student Paper Contest - Entry Date: March 16, 2012 Kevin L. Wininger 1080 Polaris Parkway, Suite 200 Columbus, OH 43240 ph: (614) 468-0300 fax: (614) 468-0212 email:
[email protected] This paper represents original research for: MATH 3540 - History and Philosophy of Mathematics, Otterbein University Fall Semester, 2011 Otterbein University 1 South Grove Street Westerville, OH 43081 ph: (614) 890-3000 1 2 On the Foundations of X-Ray Computed Tomography in Medicine: A Fundamental Review of the `Radon transform' and a Tribute to Johann Radon Abstract Objective: To acknowledge the work and life of the Austrian mathematician Johann Radon, motivated by a his- torical 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 collabo- ration 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.