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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).
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Gas water heaters cost between $600 and $2,700 to replace, for an average cost of about $1,650. Electric water heaters cost between $600 and $3,500 to replace, for an average cost of about $2,100 ...
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.
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 ...
Cartan introduced another way of constructing Haar measure as a Radon measure (a positive linear functional on compactly supported continuous functions), which is similar to the construction above except that , , and are positive continuous functions of compact support rather than subsets of .
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