Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
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gives the inverse discrete Radon transform of image.

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 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.
• 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 Method 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 (default) (.54+.46Cos[#Pi])& Hamming filter Sqrt[1/(1+#^(2n))]& Butterworth filter of order n None no filtering
• With Method->{filter,"CutoffFrequency"->f}, frequency values greater than f are set to zero. By default, no cutoff is applied.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Inverse Radon transform of a sinogram:

 Out[1]=