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A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner. Recent developments have seen the Radon transform and its inverse used for tasks related to realistic object insertion required for testing and evaluating computed tomography use in ...
Hounsfield's prototype CT scanner A historic EMI-Scanner Mark I, alongside the minicomputer used to process the CT image data. The history of X-ray computed tomography (CT) dates back to at least 1917 with the mathematical theory of the Radon transform.
Radon transform. Maps f on the (x, y)-domain to Rf on the (α, s)-domain.. In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line.
Take a two-dimensional function f(r), project (e.g. using the Radon transform) it onto a (one-dimensional) line, and do a Fourier transform of that projection. Take that same function, but do a two-dimensional Fourier transform first, and then slice it through its origin, which is parallel to the projection line. In operator terms, if
In conventional CT machines, an X-ray tube and detector are physically rotated behind a circular shroud (see the image above right). An alternative, short lived design, known as electron beam tomography (EBT), used electromagnetic deflection of an electron beam within a very large conical X-ray tube and a stationary array of detectors to achieve very high temporal resolution, for imaging of ...
However, essential mathematics and reconstruction algorithms used for CT and OPT are similar; for example, radon transform or iterative reconstruction based on projection data are used in both medical CT scan and OPT for 3D reconstruction. Both medical CT and OPT compute 3D volumes based on transmission of the photon through the material of ...
In higher dimensions, the X-ray transform of a function is defined by integrating over lines rather than over hyperplanes as in the Radon transform. The X-ray transform derives its name from X-ray tomography (used in CT scans ) because the X-ray transform of a function ƒ represents the attenuation data of a tomographic scan through an ...
Larry Janesky was born in Bridgeport Connecticut in 1964. Active in boy scouts, he earned the Eagle Scout rank at age 14. He graduated high school at age 17 in 1982 from Bullard-Havens Technical High School located in Bridgeport, CT. He did not go to college but immediately began his career as a self-employed carpenter remodeling and building ...