Shepp–Logan phantom

Short description: Standard test image

Image of the Shepp–Logan Phantom

The Shepp–Logan phantom is a standard test image created by Larry Shepp and Benjamin F. Logan for their 1974 paper "The Fourier Reconstruction of a Head Section".[1] It serves as the model of a human head in the development and testing of image reconstruction algorithms.[2][3][4]

## Definition

The function describing the phantom is defined[1] as the sum of 10 ellipses inside a 2×2 square:

Ellipse | Center | Major Axis | Minor Axis | Theta | Gray Level

|
|
|
|
|

a | (0,0) | 0.69 | 0.92 | 0 | 2
b | (0,−0.0184) | 0.6624 | 0.874 | 0 | −0.98
c | (0.22,0) | 0.11 | 0.31 | −18° | −0.02
d | (−0.22,0) | 0.16 | 0.41 | 18° | −0.02
e | (0,0.35) | 0.21 | 0.25 | 0 | 0.01
f | (0,0.1) | 0.046 | 0.046 | 0 | 0.01
g | (0,−0.1) | 0.046 | 0.046 | 0 | 0.01
h | (−0.08,−0.605) | 0.046 | 0.023 | 0 | 0.01
i | (0,−0.605) | 0.023 | 0.023 | 0 | 0.01
j | (0.06,−0.605) | 0.023 | 0.046 | 0 | 0.01

## References

1. ↑ 1.0 1.1 Shepp, Larry A.; Logan, Benjamin F. (June 1974). "The Fourier Reconstruction of a Head Section". IEEE Transactions on Nuclear Science NS-21 (3): 21–43. doi:10.1109/TNS.1974.6499235. Bibcode: 1974ITNS...21...21A. http://stat.wharton.upenn.edu/~shepp/publications/33.pdf.
2. ↑ Ellenberg, Jordan (February 22, 2010). "Fill in the Blanks: Using Math to Turn Lo-Res Datasets Into Hi-Res Samples". Wired. https://www.wired.com/magazine/2010/02/ff_algorithm. Retrieved 31 May 2013.
3. ↑ Müller, Jennifer L.; Siltanen, Samuli (2012-11-30). Linear and Nonlinear Inverse Problems with Practical Applications. SIAM. pp. 31–. ISBN 978-1-61197-233-7. https://books.google.com/books?id=P62t2uxPEYAC&pg=PA31. Retrieved 31 May 2013.
4. ↑ Koay, Cheng Guan; Sarlls, Joelle E.; Özarslan, Evren (2007). "Three-Dimensional Analytical Magnetic Resonance Imaging Phantom in the Fourier Domain". Magnetic Resonance in Medicine 58: pp. 430–436. Archived from the original on 2013-02-16. https://web.archive.org/web/20130216192913/http://stbb.nichd.nih.gov/pdf/koayMRM07.pdf.

## See also

* Imaging phantom

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