Synthesized answer
The fundamental mathematical problem behind CT scans is an inverse problem [Passage 1, Passage 2]. Specifically, if the values of the integral of a two- or three-dimensional function along all possible cross-sections are known, the challenge is to reconstruct the function itself [Passage 2].
This problem was studied by Johann Radon in the early twentieth century [Passage 2]. Allan McLeod Cormack developed mathematical algorithms that could be used to create an image from X-ray data, which is a practical application of this concept [Passage 1]. Godfrey Newbold Hounsfield then designed the first operational CT scanner based on this principle [Passage 1]. The passages do not explain other key concepts in my own words.
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
Title: The Mathematics of Medical Imaging by Timothy G. Feeman Description: In 1979, the Nobel Prize for Medicine and Physiology was awarded jointly to Allan McLeod Cormack and Godfrey Newbold Houns eld, the two pioneering scienti- engineers primarily responsible for the development, in the 1960s and early 1970s, of computerized axial tomography, popularly known as the CAT or CT scan. In his papers [13], Cormack, then a Professor at Tufts University, in Massachusetts, dev- oped certain mathematical algorithms that, he envisioned, could be used to create an image from X-ray data. Working…
nd this procedure is essentially mathematical: If we know the values of the integral of a two- or three-dimensional fu- tion along all possible cross-sections, then how can we reconstruct the function itself? This particular example of what is known as an inverse problem was studied by Johann Radon, an Austrian mathematician, in the early part of the twentieth century. Categories: Mathematics Pages: 151 Snippet: ... Mathematics 32 , SIAM , Philadelphia , 2001 . 31. Noble , B. , and J. W. Daniel , Applied Linear Algebra , 3rd ed . , Prentice - Hall , Englewood Cliffs , 1988 . 32. <b>The…