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InverseRadon

InverseRadon[image]
gives the inverse discrete Radon transform of image.
InverseRadon
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:
In[1]:=
Click for copyable input
Out[1]=
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