BUILT-IN MATHEMATICA SYMBOL

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 /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.
• 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 None no 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.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Inverse Radon transform of a sinogram:

 Out[1]=