Shepp–Logan phantom

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:

EllipseCenterMajor AxisMinor AxisThetaGray Level
a(0,0)0.690.9202
b(0,−0.0184)0.66240.8740−0.98
c(0.22,0)0.110.31−18°−0.02
d(−0.22,0)0.160.4118°−0.02
e(0,0.35)0.210.2500.01
f(0,0.1)0.0460.04600.01
g(0,−0.1)0.0460.04600.01
h(−0.08,−0.605)0.0460.02300.01
i(0,−0.605)0.0230.02300.01
j(0.06,−0.605)0.0230.04600.01

References

  1. 1 2 Shepp, Larry A.; Logan, Benjamin F. (June 1974). "The Fourier Reconstruction of a Head Section" (PDF). IEEE Transactions on Nuclear Science. NS-21 (3): 21–43. Bibcode:1974ITNS...21...21A. doi:10.1109/TNS.1974.6499235. Archived from the original (PDF) on 2016-03-04.
  2. Ellenberg, Jordan (February 22, 2010). "Fill in the Blanks: Using Math to Turn Lo-Res Datasets Into Hi-Res Samples". Wired. 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. 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" (PDF). Magnetic Resonance in Medicine. 58. pp. 430–436. Archived from the original (PDF) on 2013-02-16.

See also


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