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To create a simulated phantom sinogram, it is common to firstly create the 2-d digital image:

I = phantom(xxx);

and then apply the rand() transform

R = radon(I, theta);

However, since the phantom image has its analytical expression, it will be more accurate to simulate the parallel projection if the radon transform is performed on the analytical expression, i.e., on the analog image directly.

Is it possible in Matlab?

lxg
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1 Answers1

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How would it be more accurate? Much of the artifacts are either caused or amplified by the discrete CT-datasets. The point of the phantom is usually to study these artifacts. All of the algorithms that I have seen have been discrete, all of the results everywhere are from discrete datasets with discrete algorithms. I'd keep with the crowd.

You can find the analytical expression for the radon transform for the Shepp-Logan phantom from Peter Toft's PhD (http://orbit.dtu.dk/files/5529668/Binder1.pdf), pages 199-201

... Due to the constant excitation on the circle the Radon transform is merely the length of the line crossing the circle ...

If Q ellipses are given with a set of parameters then due to the linearity the Radon transform is a sum ...

The analytical expression for the phantom itself can be found from Wikipedia, or the original article if you wish to cite it:

L. A. Shepp and B. F. Logan, Bell Laboratories, THE FOURIER RECONSTRUCTION OF A HEAD SECTION, IEEE TRANSACTION ON NUCLEAR SCIENCE,VOL.NS-21, JUNE 1974

Tunaki
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Tapio
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  • I have implemented the code according to the analytical expressions. Nevertheless, Thank you. – lxg Sep 04 '16 at 16:39
  • For practical CT data, each projection sample is a line integral in analog manner. On the other hand, for the phantom, since there is analytical expression, while discrete Radon transform may introduce errors due to approximation matter. Therefore, I guess that the analytical expression may be more accurate. I have implemented the code according to the analytical expressions. Nevertheless, Thank you. – lxg Sep 04 '16 at 16:45