X-ray Transform and Reconstruction: stomach

We use a program xray.jl, which I found on the internet. However, I am very sorry to forget who constructed this program. This file was for older version of the Julia Programming Language and I change "radon" of xray.jl. The unfiltered and filtered back-projections are obtained by my own program. See stomach.jl for the detail.

All in One
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.