Summary
The Princeton Companion to Mathematics presents the mathematical underpinnings of modern medical imaging technologies. It highlights how inverse problems, specifically the reconstruction of a function from its cross-sectional integrals, are central to techniques like computerized axial tomography (CAT or CT scans). The work of Johann Radon, Allan McLeod Cormack, and Godfrey Newbold Hounsfield exemplifies this mathematical challenge.
Readers will learn that procedures like CT scanning, responsible for millions of medical diagnoses annually, rely on sophisticated mathematical algorithms developed in the mid-20th century. The companion elucidates the theoretical basis for creating images from data such as X-ray measurements, demonstrating the direct application of abstract mathematical concepts to practical, life-saving technologies.
Key concepts
- Inverse problem — The task of reconstructing a function when only information about its integrals along various cross-sections is known.
- Johann Radon — An Austrian mathematician who studied the problem of reconstructing a function from its cross-sectional integrals in the early 20th century.
- Computerized axial tomography (CAT or CT scan) — A medical imaging technique whose development in the 1960s and 1970s was fundamentally based on mathematical algorithms.
- Allan McLeod Cormack — Developed mathematical algorithms to create images from X-ray data for CT scans.
- Godfrey Newbold Hounsfield — Designed the first operational and commercially available CT scanner.
From the book
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 completely independently of Cormack and at about the same time, Houns eld, a research scientist at EMI Central Research Laboratories in the United Kingdom, designed the rst operational CT scanner as well as the rst commercially available model. (See [22] and [23]. )…
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 Princeton Companion to Mathematics</b> , T. <b>Gowers</b> , <b>Editor</b> , Princeton ...