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Three Dimensional Analytical Magnetic Resonance Imaging Phantom in the Fourier Domain

version 1.1 (2.32 MB) by

This software contains 2D and 3D Shepp-Logan phantoms in both the image and Fourier domains.



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This submission contains a collection of codes in different programming languages that implement the analytical framework proposed in

Koay CG, Sarlls JE, Özarslan E.
 * Three Dimensional Analytical Magnetic Resonance Imaging Phantom in the Fourier Domain. Magn Reson Med. 58: 430-436 (2007)

The article above can be obtained from:

Comments and Ratings (10)

There are many different conventions for the Euler angles. The one adopted here is consistent with the paper and achieved the desired results in terms of the orientation of the ellipsoids.

Pankaj Daga

I think in the 3D Shepp Logan code, the rotation matrices are not generated correctly. The Rx matrix should be used instead of using the Rz matrix twice.

Sorry, I had problems with the comment submission. I accidentally deleted an earlier message that contained my explanations.

I shall try to explain it again here.

The first thing I should point out is that the field-of-view (FOV) in the image domain is fixed. Each FOV in each dimension is two units (arbitrary unit) from -1 to 1. Therefore, the resolution along the x-axis, denoted as del_x, in the image domain is determined by the number of samples, N, and it is given by del_x = FOV/N.

The resolution along the k-axis, denoted as del_kx, in the Fourier domain is determined by the FOV, and it is given by del_kx = 1/FOV.

The main thing is to know how wide one should sample the k-space or Fourier domain. The magnitude of k_max, i.e., |k_max| is given by del_kx * N/2 . Note that it is assumed that the negative and the positive regions are sampled equally.

So, "K<0.002" should not be the problem. Hope this helps. If not, feel free to email.


I forgot to say that there is no problem with K<0.002. :)


First of all really nice work!!! I have just a question the package work well for an image resolution equal or higher 128x128X128, for lower resolution the signal in kspace is not numerically avoid this problem is it sufficient to change the condition on K<0.002, or i have to do something else???

Thank you

In the revised SampleTest.m, I used imtool and please make sure that you click on a menu that allows you to change contrast. min=0.0 and max=3.0 should be fine and these values should be applied to both imtool panels.

Due the inconvenience of updating and commenting on the site, I have decided to only update the site with major releases.

The MATLAB codes that illustrate the steps needed to perform FFT on the k-space signals of the 3D Shepp-Logan phantom can be found in a revised version of SampleTest.m, which is located on my google site:

Jay Rod

This package is very useful for testing MRI image reconstruction and simulation studies. 2D and 3D Shepp-Logan phantoms in the Fourier domain and image domain are critical to analysis in magnetic resonance imaging. Excellent extensible Java source codes with useful MATLAB, Mathematica, and IDL interfaces. Thanks a lot for sharing the source codes and your paper.


John (view profile)



Added 2D Fourier domain phantom and a feature that allows users to change the properties of the phantom.

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