title: Shepp–Logan phantom
text: # 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. It serves as the model of a human head in the development and testing of image reconstruction algorithms.
  
  ## 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 |
  