(*by Nasser M. Abbasi, updated 9/22/14*)
Manipulate[
 ImageAdjust@InverseRadon[Radon[img, {n, n}, Method -> method],
    "Filter" -> inverseMethod, "CutoffFrequency" -> cutOffFrequency]
 ,
 Grid[{
   {Control[{{cutOffFrequency, 1, Text@Row[{Subscript[Style["f", Italic, 11], Style["c", Italic, 11]]}]}, .01, 1, 0.01,
      ImageSize -> Small, Appearance -> "Labeled"}]},
   {Control[{{method, "Radon", "Radon method"}, {"Radon", "Hough"}, ControlType -> PopupMenu, ImageSize -> All}]},
   {
    Control[{
      {inverseMethod, # Cos[# Pi] &, "Inverse Radon method"},
      {(1 + Cos[# Pi])/2 & -> "Hann",
       1 & -> "Rectangular",
       # & -> "Ramp-Lak",
       # Sin[# 2 Pi] & -> "Sin Ramp",
       # Cos[# Pi] & -> "Cosine Ramp",
       ((1 - 0.16)/2 - (1/2) Cos[# Pi] + 0.08 Cos[# 2 Pi]) & -> "Blackman",
       (0.355768 - 0.487396 Cos[# Pi] + 0.144232 Cos[# 2 Pi]) - 0.012604 Cos[# 3 Pi] & -> "Nuttal window",
       Sinc[#] & -> "Shepp-Logan",
       (.54 + .46 Cos[# Pi]) & -> "Hamming",
       Sqrt[1/(1 + #^(2))] & -> "Butterworth order 1",
       Sqrt[1/(1 + #^(4))] & -> "Butterworth order 2",
       Sqrt[1/(1 + #^(6))] & -> "Butterworth order 3",
       None -> "No filter"},
      ControlType -> PopupMenu, ImageSize -> All}]
    }}],
 ContinuousAction -> False,
 Initialization :>
  (
   n = 200;(*image size ti display*)
   img = ExampleData[{"TestImage", "Lena"}];
   )
 ]