Search results
Results from the WOW.Com Content Network
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.
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 ...
The history of X-ray computed tomography (CT) dates back to at least 1917 with the mathematical theory of the Radon transform. [1] [2] In the early 1900s an Italian radiologist named Alessandro Vallebona invented tomography (named "stratigrafia") which used radiographic film to see a single slice of the body.
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 F 1 and F 2 are the 1- and 2-dimensional Fourier transform operators mentioned above, P 1 is the projection operator (which projects a 2-D function onto a 1-D line),
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 ...
The Mojette transform is an application of discrete geometry. More specifically, it is a discrete and exact version of the Radon transform, thus a projection operator. The IRCCyN laboratory - UMR CNRS 6597 in Nantes, France has been developing it since 1994. The first characteristic of the Mojette transform is using only additions and subtractions.
John's equation is an ultrahyperbolic partial differential equation satisfied by the X-ray transform of a function. It is named after German-American mathematician Fritz John . Given a function f : R n → R {\displaystyle f\colon \mathbb {R} ^{n}\rightarrow \mathbb {R} } with compact support the X-ray transform is the integral over all lines ...
No. 2 Georgia is resting its national championship hopes on backup quarterback Gunner Stockton following Carson Beck's season-ending elbow surgery on Monday. Coach Kirby Smart said Monday that ...