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In theory, the inverse Radon transformation would yield the original image. The projection-slice theorem tells us that if we had an infinite number of one-dimensional projections of an object taken at an infinite number of angles, we could perfectly reconstruct the original object, f ( x , y ) {\displaystyle f(x,y)} .
Laguerre transform; Laplace transform. Inverse Laplace transform; Two-sided Laplace transform; 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 ...
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 "twistor space" Z is complex projective 3-space CP 3, which is also the Grassmannian Gr 1 (C 4) of lines in 4-dimensional complex space. X = Gr 2 (C 4), the Grassmannian of 2-planes in 4-dimensional complex space. This is a compactification of complex Minkowski space. Y is the flag manifold whose elements correspond to a line in a plane of C 4.
A real-valued Radon measure is defined to be any continuous linear form on K (X); they are precisely the differences of two Radon measures. This gives an identification of real-valued Radon measures with the dual space of the locally convex space K (X). These real-valued Radon measures need not be signed measures.
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6.1.3 Test functions as distributions. ... 6.4.3 Fourier transform. ... Download as PDF; Printable version; In other projects
For example, if f represented mass density and μ was the Lebesgue measure in three-dimensional space R 3, then ν(A) would equal the total mass in a spatial region A. The Radon–Nikodym theorem essentially states that, under certain conditions, any measure ν can be expressed in this way with respect to another measure μ on the same