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Projection-slice theorem - Wikipedia
https://en.wikipedia.org/wiki/Projection-slice_theorem
In mathematics, the projection-slice theorem, central slice theorem or Fourier slice theorem in two dimensions states that the results of the following two calculations are equal: 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 … See more
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Slice Theorem - an overview | ScienceDirect Topics
https://www.sciencedirect.com/topics/engineering/slice-theorem
WebThe projection– slice theorem is used to collect the data in the Fourier domain, and then the inverse Fourier transform is performed (by FFT) to reconstruct the absorption …
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Projection-slice theorem - HandWiki
https://handwiki.org/wiki/Projection-slice_theorem
The Projection-Slice Theorem in N DimensionsThe Generalized Fourier-Slice TheoremProof in Two DimensionsThe FHA CycleExtension to Fan Beam Or Cone-Beam CtFurther ReadingExternal Links The projection-slice theorem is easily proven for the case of two dimensions.Without loss of generality, we can take the projection line to be the x-axis.There is no loss of generality because if we use a shifted and rotated line, the law still applies. Using a shifted line (in y) gives the same projection and therefore the same 1D Fourier transfor...
The projection-slice theorem is easily proven for the case of two dimensions.Without loss of generality, we can take the projection line to be the x-axis.There is no loss of generality because if we use a shifted and rotated line, the law still applies. Using a shifted line (in y) gives the same projection and therefore the same 1D Fourier transfor...
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The Projection-Slice Theorem | SpringerLink
https://link.springer.com/chapter/10.1007/978-1-4419-8963-5_14
WebThe Projection-Slice Theorem Ronald Bracewell Chapter 1131 Accesses Abstract When a function has circular symmetry, its two-dimensional Fourier transform can be expressed … Author: Ronald Bracewell Publish Year: 2003
Author: Ronald Bracewell
Publish Year: 2003
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Projection-Slice Theorem for Fourier series - Mathematics …
https://math.stackexchange.com/questions/2857743/projection-slice-theorem-for-fourier-series
WebJul 20, 2018 · Such a function has a Fourier series representation and there should be a relationship between projections of Fourier coefficients and slices of the function. …
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Projection-slice theorem - formulasearchengine
https://www.formulasearchengine.com/wiki/Projection-slice_theorem
WebS 1 is a slice operator (which extracts a 1-D central slice from a function), then: = This idea can be extended to higher dimensions. This theorem is used, for example, in the analysis …
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1: The Fourier projection-slice theorem states that a slice …
https://www.researchgate.net/figure/The-Fourier-projection-slice-theorem-states-that-a-slice-extracted-from-the-frequency_fig1_250918146
Web1: The Fourier projection-slice theorem states that a slice extracted from the frequency domain representation of a 3D volume yields the Fourier transform of a projection of the volume in a...
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Radon transform - Wikipedia
https://en.wikipedia.org/wiki/Radon_transform
WebIn 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 …
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Projection Slice Theorem - [PDF Document]
https://vdocuments.net/projection-slice-theorem.html
WebNov 22, 2015 · PROJECTION SLICE THEOREM HOW TO USE THE PROJECTION SLICE THEOREM FOR 2 D IMAGES Take a 2D function fx of the image Project it onto a …
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image processing - Implementing a filtered …
https://stackoverflow.com/questions/61260808/implementing-a-filtered-backprojection-algorithm-using-the-central-slice-theorem
WebImplementing a filtered backprojection algorithm using the central slice theorem in Matlab. I'm working on a filtered back projection algorithm using the central slice theorem for a homework assignment and while I …
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