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 transform was introduced in 1917 by Johann Radon,[1] who also provided a formula for the inverse transform. Radon further included formulas for the transform in three dimensions, in which the integral is taken over planes (integrating over lines is known as the X-ray transform). It was later generalized to higher-dimensional Euclidean spaces and more broadly in the context of integral geometry. The complex analogue of the Radon transform is known as the Penrose transform. The Radon transform is widely applicable to tomography, the creation of an image from the projection data associated with cross-sectional scans of an object.
In mathematics, the Radontransform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional)...
Hough transform conceptually very close to the two-dimensional Radontransform. In fact, the Hough transform is mathematically equivalent to the Radon transform...
so-called Radon–Riesz property. Radon spaces Radonifying function Brigitte Bukovics: Biography of Johann Radon, in: 75 Years of RadonTransform, S. Gindikin...
dimensions. Abel transform can be viewed as the Radontransform of an isotropic 2D function f(r). As f(r) is isotropic, its Radontransform is the same at...
obtained in non-invasive manner. Recent developments have seen the Radontransform and its inverse used for tasks related to realistic object insertion...
geometry, the Funk transform (also known as Minkowski–Funk transform, Funk–Radontransform or spherical Radontransform) is an integral transform defined by integrating...
The Mojette transform is an application of discrete geometry. More specifically, it is a discrete and exact version of the Radontransform, thus a projection...
(Hanzi), especially when used in a different language Radontransform, a type of integral transform in mathematics A visual representation of the raw data...
tomography dates back to at least 1917 with the mathematical theory of the Radontransform In the early 1900s an Italian radiologist named Alessandro Vallebona...
In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration...
space. Such transformations often take the form of integral transforms such as the Radontransform and its generalizations. Integral geometry as such first...
(s,θ) obtained by performing radontransform to μ(x, y), and (2)μ(x, y) is restored by performing inverse radontransform to measurement results. Consider...
theoretical physics, the Penrose transform, introduced by Roger Penrose (1967, 1968, 1969), is a complex analogue of the Radontransform that relates massless fields...
differential equations and ill-posed problems. His early work was on the Radontransform and he is remembered for John's equation. He was a 1984 MacArthur Fellow...
CT reconstructions, in that they are based on performing an inverse Radontransform. Due to partial data sampling with very few projections, approximation...
equation). This is essentially a form of the inversion formula for the Radontransform because it recovers the value of φ(x) from its integrals over hyperplanes...
singularity theorem in general relativity Penrose transform, a complex analogue of the Radontransform in theoretical physics Penrose–Ward correspondence...
Johann Radon Medical imaging MRI compared with CT Network tomography Nonogram, a type of puzzle based on a discrete model of tomography Radontransform Tomographic...
tomography goes back to at least 1917 with the mathematical theory of the Radontransform. In October 1963, William H. Oldendorf received a U.S. patent for a...
series See also list of transforms, list of Fourier-related transforms Kernel (integral operator) Convolution Radontransform Buffon's needle Hadwiger's...
Encyclopedia of Mathematics". L. Ehrenpreis, The Universality of the RadonTransform, Oxford Univ. Press, 2003. Gromov, M. (1986), Partial differential...
Radontransform. Although from a theoretical point of view many linear inverse problems are well understood, problems involving the Radontransform and...
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