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.
Radon is known for a number of lasting contributions, including: his part in the Radon–Nikodym theorem; the Radon measure concept of measure as linear functional; the Radon transform, in integral geometry, based on integration over hyperplanes—with application to tomography for scanners (see tomographic reconstruction);
Inverse two-sided Laplace transform; Laplace–Carson transform; Laplace–Stieltjes transform; Legendre transform; Linear canonical transform; Mellin transform. Inverse Mellin transform; Poisson–Mellin–Newton cycle; N-transform; Radon transform; Stieltjes transformation; Sumudu transform; Wavelet transform (integral) Weierstrass transform ...
In the mathematical field of integral geometry, the Funk transform (also known as Minkowski–Funk transform, Funk–Radon transform or spherical Radon transform) is an integral transform defined by integrating a function on great circles of the sphere. It was introduced by Paul Funk in 1911, based on the work of Minkowski (1904).
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
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.
In practice of tomographic image reconstruction, often a stabilized and discretized version of the inverse Radon transform is used, known as the filtered back projection algorithm. [2] With a sampled discrete system, the inverse Radon transform is
In X-ray computed tomography the lines on which the parameter is integrated are straight lines: the tomographic reconstruction of the parameter distribution is based on the inversion of the Radon transform. Although from a theoretical point of view many linear inverse problems are well understood, problems involving the Radon transform and its ...