InverseRadon

InverseRadon[image]
gives the inverse discrete Radon transform of image.

InverseRadon[image, {w, h}]
specifies the width w and the height h of the resulting image.

Details and OptionsDetails and Options

  • 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[image, w] is equivalent to InverseRadon[image, {w, w}].
  • By default, InverseRadon[image, ...] computes one back projection for each column in image. InverseRadon[image, {w, h}, n] uses n back projections.
  • 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.
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