Shepp–Logan phantom explained
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 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 | |
See also
Notes and References
- Shepp. Larry A. . Logan . Benjamin F. . The Fourier Reconstruction of a Head Section . June 1974 . . NS-21 . 3 . 21–43 . 10.1109/TNS.1974.6499235. https://web.archive.org/web/20160304035526/http://stat.wharton.upenn.edu/~shepp/publications/33.pdf . 2016-03-04. 1974ITNS...21...21A .
- News: Fill in the Blanks: Using Math to Turn Lo-Res Datasets Into Hi-Res Samples . Ellenberg . Jordan . February 22, 2010 . . 31 May 2013.
- Book: Müller . Jennifer L. . Siltanen . Samuli . Linear and Nonlinear Inverse Problems with Practical Applications . 31 May 2013 . 2012-11-30 . SIAM . 978-1-61197-233-7 . 31–.
- News: Koay . Cheng Guan . Joelle E. . Sarlls . Evren . Özarslan . Three-Dimensional Analytical Magnetic Resonance Imaging Phantom in the Fourier Domain . 2007 . . 58 . 430–436 . dead . https://web.archive.org/web/20130216192913/http://stbb.nichd.nih.gov/pdf/koayMRM07.pdf . 2013-02-16 .
