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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.
Tomographic reconstruction: Projection, Back projection and Filtered back projection. Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections.
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).
These first Heisler–Gröber charts were based upon the first term of the exact Fourier series solution for an infinite plane wall: (,) = = [ + ], [1]where T i is the initial uniform temperature of the slab, T ∞ is the constant environmental temperature imposed at the boundary, x is the location in the plane wall, λ is the root of λ * tan λ = Bi, and α is thermal diffusivity.
The fifth is a high-resolution Linear Radon transformation performed by Luo et al. (2008). [10] In performing a wave-field transformation, a slant stack is done, followed by a Fourier transform . The way in which a Fourier transform changes x-t data into x-ω (ω is angular frequency) data shows why phase velocity dominates surface wave ...
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 ...
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The Radon transform can be viewed as a measure-theoretic generalization of the Crofton formula and the Crofton formula is used in the inversion formula of the k-plane Radon transform of Gel'fand and Graev [4] Steinhaus longimeter