An Example of X-ray Transform and Reconstruction 1

1. Original RGB Data 2. Conversion of RGB Data to Gray Scale Image
3. Complementation 4. X-ray transform of 3
5. Unfiltered Back Projection of 4 6. Reconstruction, i.e., Filtered Back Projection of 4
"Unfiltered back projection" is called "Back Projection" which is mathematically the dual X-ray transform. "Filtered back projection" is so-called the reconstruction formula for the X-ray transform mathematically, that is, the back projection applied by the filter which is mathematically the square root of the nonnegative Laplacian on the plane.