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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.
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).
In N dimensions, the projection-slice theorem states that the Fourier transform of the projection of an N-dimensional function f(r) onto an m-dimensional linear submanifold is equal to an m-dimensional slice of the N-dimensional Fourier transform of that function consisting of an m-dimensional linear submanifold through the origin in the Fourier space which is parallel to the projection ...
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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.
A typical radon test kit Fluctuation of ambient air radon concentration over one week, measured in a laboratory. The first step in mitigation is testing. No level of radiation is considered completely safe, but as it cannot be eliminated, governments around the world have set various action levels to provide guidance on when radon concentrations should be reduced.
Natural radon concentrations in the Earth's atmosphere are so low that radon-rich water in contact with the atmosphere will continually lose radon by volatilization. Hence, ground water has a higher concentration of 222 Rn than surface water , because radon is continuously produced by radioactive decay of 226 Ra present in rocks.
In many situations the basic strategy is to apply the Fourier transform, perform some operation or simplification, and then apply the inverse Fourier transform. More abstractly, the Fourier inversion theorem is a statement about the Fourier transform as an operator (see Fourier transform on function spaces).