X-ray Transform and Reconstruction: half plane

See half_plane_a.m and half_plane_b.m for the detail.

Original Grayscale Image X-ray transform
Unfiltered Backprojection Reconstruction, i.e., Filtered Backprojection
"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.