Shepp–Logan phantom

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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[edit]

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[edit]

  1. ^ a b 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. 

See also[edit]