# Which filter does InverseRadon use by default?

I am using the InverseRadon function. According to the documentation the function uses a Hann filter and no cutoff ("CutoffFrequency"->1) by default. However, if this is given as an option the result is different from the default.

Is their a way to determine which parameters (Filter and cutoff) are used by default?

I have tested the filters listed in the documentation. The result is closest to the cosine-ramp filter, but not identical.

i = Import["http://i.imgur.com/zxKkFP9.png"];(* Sinogram from InverseRadon Documentation *)
filter = {{Automatic, "Default"}, {#1&, "ramp filter with constant slope"},{#1 Cos[#1 \[Pi]]&, "ramp filter multiplied by cosine function"}, {(1+Cos[#1 \[Pi]])/2&, "Hann filter (default)"}, {0.54 +0.46 Cos[#1 \[Pi]]&, "Hamming filter"}, {Sqrt[1/(1+#^(2n))]&, Row@{"Butterworth filter of order ",n}}, {1&, "no filtering"}};


Edit: I have tested @JM's suggestion to use the scaled cosine-ramp filter.

ImageDifference@@(ImageAdjust@InverseRadon[i, {300, 300}, Method -> #] & /@ {Automatic, (# (1 + Cos[\[Pi] #])/2 &)})


This results a black image image. The two options are almost equal, but not identical. The maximum difference (Max@ImageData) is 0.00249. This is difference image after an ImageAdjust:

• Try this: ImageAdjust[InverseRadon[i, {300, 300}, Method -> (# (1 + Cos[π #])/2 &)]]. Use ImageDifference[] to compare with the result of ImageAdjust[InverseRadon[i, {300, 300}]]. Mar 23, 2017 at 13:59
• @J.M. I Have tested your suggestion. The difference between the default and the scaled cosine-ramp filter is very minor and for me negligible. This solved my problem. Thank you.
– jct
Mar 24, 2017 at 9:35
• @jct In other words, the default setting seems to be a Ram.-Lak. (Ramp) filter multiplied by a Hann window.
– UDB
Nov 28, 2018 at 13:21