Search results
Results from the WOW.Com Content Network
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)} .
(1)Results of measurement, i.e. a series of images obtained by transmitted light are expressed (modeled) as a function p (s,θ) obtained by performing radon transform to μ(x, y), and (2)μ(x, y) is restored by performing inverse radon transform to measurement results.
Take a two-dimensional function f(r), project (e.g. using the Radon transform) it onto a (one-dimensional) line, and do a Fourier transform of that projection. Take that same function, but do a two-dimensional Fourier transform first, and then slice it through its origin, which is parallel to the projection line. In operator terms, if
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 ...
A systematic study of the singularities of the Radon transform is given, a complete description of the asymptotics of the Radon transform near a point of its singular support is obtained and applied to the important problem of tomography: finding singularities of a function from its tomographic data; these results are published in a series of ...
Tomographic reconstruction methods used in USCT systems for transmission information based imaging are classical inverse radon transform and fourier slice theorem and derived algorithms (cone beam etc.). As advanced alternatives, ART-based approaches are also utilized.
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field.