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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.
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); Radon's theorem, that d + 2 points in d dimensions may always be partitioned into two subsets with intersecting convex hulls;
Sigma algebra. Separable sigma algebra; ... Radon transform; Integral geometry ... This page was last edited on 2 May 2022, ...
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
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),
John, Fritz (1955), Plane waves and spherical means applied to partial differential equations, Interscience Tracts in Pure and Applied Mathematics, vol. 2 (1st ed.), New York: Interscience Publishers, pp. VIII+172, MR 0075429, Zbl 0067.32101. John's famous monograph on the Radon transform and its application to partial differential equations.
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 ...
3.3.2 Topology on the space of distributions and its relation to the weak-* topology. ... 6.1 Radon measures. ... 6.4 Tempered distributions and Fourier transform.
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