This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


gives the inverse discrete Radon transform of image.
specifies the width w and the height h of the resulting image.
  • InverseRadon finds an approximation of the inverse of the Radon transform, using a filtered back projection method.
  • InverseRadon operates on an image that represents a discrete Radon transform of an image, assuming that the columns represent angles from to /2 relative to the vertical axis, and the rows represent scaled distances to the center of the output.
  • InverseRadon[image] returns a square image whose sides have the same length as the diagonal of image.
  • InverseRadon takes a option that specifies a frequency filter to be applied before computing the back projection. The domain of the filter is scaled to be 0 to 1. By default a Hann filter is used.
  • Typical filter settings include:
#&ramp filter with constant slope
#Cos[#Pi]&ramp filter multiplied by cosine function
(1+Cos[#Pi])/2&Hann filter
(.54+.46Cos[#Pi])&Hamming filter
Sqrt[1/(1+#^(2n))]&Butterworth filter of order n
Noneno filtering
  • InverseRadon accepts a option. Using the setting "CutoffFrequency"->f, frequency values greater than f are set to zero. By default no cutoff is applied.
Inverse Radon transform of a sinogram:
Inverse Radon transform of a sinogram:
Click for copyable input
Reconstruct an image of a specific size:
Specify the number of back projections:
Use smaller cutoff frequency to get a smoother image:
Reconstruct line segments from the result of a Radon transform:
Compute the inverse of the Radon transform:
Inverse Radon transform of a horizontal line:
New in 8