Talk:Tomographic reconstruction

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Figure indices need review

Apart from fig. 1, the indices are missing, and perhaps not correct. — Preceding unsigned comment added by 134.158.85.214 (talk) 14:01, 14 February 2017 (UTC)[reply]

Mistake in "r" expression?

Did I forget my elementary maths or on figure 1: $r=\pm {\sqrt {(x.\cos \theta )^{2}+(y.\sin \theta )^{2}}}$ instead of $r=x.\cos \theta +y.\sin \theta$ ? 12:22, 13 February 2014 (UTC)212.186.248.10 (talk) 12:22, 13 February 2014 (UTC)[reply]
I'm not sure which distance you like to characterize with your formula. It looks to me like the radius of a centered circle.
In my opinion the picture is described insufficient and some more explanations would be good in general.
Eg. I assume that right in the first formula "I" stands for intensity, but nobdoy found it worth to mention.
Or it makes it more difficult that r is used in the pircture for a signed distance but also for a coordinate

The formula

x\cos \theta +y\sin \theta =r\

describes the line that is marked with AB, in reference to the xy coordinate system.
θ is the angle of AB
r is the displacement of the line AB from the point of origin
My assumptions to the picture:
The line AB is normal to the projection plain.
The point of the xy origin represents the middle of the machine
The line AB represents the ray which is moved into direction of coordinate r.
The distance r is a signed distance. It changes the sign when AB passes the point of origin.

Don't

Don't you think that Radon's transformation is just one of methods used in tomographic reconstruction? Saigon from europe 21:28, 2 Jun 2005 (UTC)

The Radon Transform simply describes the physical process in mathematical terms. Reconstruction means solving for f 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, such as the Fourier Transform, and other methods rely or linear algebra, and (many more methods). Frade 00:19, 12 January 2006 (UTC)[reply]

But in this case, these other methods should be mentioned in the article.

In SPECT reconstruction, where a tomographic reconstruction is also used, iterative reconstruction methods like OSEM and MLEM have replaced filtered backprojection.

Isn't therefore the name "tomographic reconstruction" a bit misleading? --Hg6996 (talk) 09:23, 16 January 2009 (UTC)[reply]

Images

These images were posted at the sinogram 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 ... Agradman (talk) 18:36, 13 June 2009 (UTC)[reply]

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).

Phantom image, two kitty-corner squares.

Needs to be rewritten by an expert

I am a mathematician, but I found this article confusing to the point of being useless. In the diagram, the letter r 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.

This is far from my areas of expertise, so I am unable to attempt a fix. Someone please tag this article.

-- Solo Owl 18:04, 1 July 2014 (UTC)

Gallery contains wrong statement

The "ART based reconstruction" video is definitely an example of a filtered-backprojection where the backprojection is visualized step by step. — Preceding unsigned comment added by 2003:CA:A3E2:8000:4134:5826:CCE4:E3D9 (talk) 21:22, 8 October 2016 (UTC)[reply]

What is delta?

In this equation,

p_{\theta }(r)=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\delta (x\cos \theta +y\sin \theta -r)\,dx\,dy

what is $\delta$ ? MathPerson (talk) 14:26, 15 October 2019 (UTC)[reply]

Thanks for pointing that out. It is the Dirac delta function. I have added a link in the article. --{{u|Mark viking}} {Talk} 17:59, 15 October 2019 (UTC)[reply]