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inside the integral in the Radon
Transform. It is unusual to use Radon's Inverse Transform to do this, for the reasons given in the article, hence many other methods are available. Some of these other methods rely on the relationship of the Radon Transform with other mathematical transformations,
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is used for two entirely different objects, and it has yet a third different use in the alleged explanation. The formulas are not explained adequately. I make no sense of it.
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In SPECT reconstruction, where a tomographic reconstruction is also used, iterative reconstruction methods like OSEM and MLEM have replaced filtered backprojection.
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Sinogram of two squares, taken at 50 equidistant angles over a 180 degree span (it is only by coincidence that the x-axis marks displacement at -50 and 50 units).
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The "ART based reconstruction" video is definitely an example of a filtered-backprojection where the backprojection is visualized step by step.
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page, but as that is a disambiguation page I thought they belonged here. Someone with expertise in the subject can post them if you want ...
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882:{\displaystyle p_{\theta }(r)=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\delta (x\cos \theta +y\sin \theta -r)\,dx\,dy}
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I'm not sure which distance you like to characterize with your formula. It looks to me like the radius of a centered circle.
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I am a mathematician, but I found this article confusing to the point of being useless. In the diagram, the letter
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Or it makes it more difficult that r is used in the pircture for a signed distance but also for a coordinate
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Eg. I assume that right in the first formula "I" stands for intensity, but nobdoy found it worth to mention.
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This is far from my areas of expertise, so I am unable to attempt a fix. Someone please tag this article.
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In my opinion the picture is described insufficient and some more explanations would be good in general.
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Don't you think that Radon's transformation is just one of methods used in tomographic reconstruction?
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Thanks for pointing that out. It is the Dirac delta function. I have added a link in the article. --
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such as the
Fourier Transform, and other methods rely or linear algebra, and (many more methods).
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on 2 April 2017. For the contribution history and old versions of the redirected page, please see
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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The distance r is a signed distance. It changes the sign when AB passes the point of origin.
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describes the line that is marked with AB, in reference to the xy coordinate system.
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the physical process in mathematical terms. Reconstruction means solving for
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The line AB represents the ray which is moved into direction of coordinate r.
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Isn't therefore the name "tomographic reconstruction" a bit misleading? --
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But in this case, these other methods should be mentioned in the article.
421:{\displaystyle r=\pm {\sqrt {(x.\cos \theta )^{2}+(y.\sin \theta )^{2}}}}
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Apart from fig. 1, the indices are missing, and perhaps not correct.
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109:. Please visit the project page for details or ask questions at
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The point of the xy origin represents the middle of the machine
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r is the displacement of the line AB from the point of origin
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555:{\displaystyle x\cos \theta +y\sin \theta =r\ }
477:{\displaystyle r=x.\cos \theta +y.\sin \theta }
105:and that biomedical information in any article
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103:Manual of Style for medicine-related articles
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118:Medicine
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