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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 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)} .
The fourth is a modified wave-field transform base on frequency decomposition and slant stacking, performed by Xia et al. (2007). [9] 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 ...
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).
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.
A water level device showing both ends at the same height. A water level (Greek: Aλφαδολάστιχο or (υδροστάθμη) [Alfadolasticho]) is a siphon utilizing two or more parts of the liquid water surface to establish a local horizontal line or plane of reference.
Santaló's formula is valid for all (). In this case it is equivalent to the following identity of measures: In this case it is equivalent to the following identity of measures: Φ ∗ d μ ( x , v , t ) = ν ( x ) , x d σ ( x , v ) d t , {\displaystyle \Phi ^{*}d\mu (x,v,t)=\langle \nu (x),x\rangle d\sigma (x,v)dt,}
In mathematics, the X-ray transform (also called ray transform [1] or John transform) is an integral transform introduced by Fritz John in 1938 [2] that is one of the cornerstones of modern integral geometry. It is very closely related to the Radon transform, and coincides with it in two dimensions.