X-ray Transform and Reconstruction: square

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 square.jl for the detail. A program scatter.jl draws the wave front sets of the characteristic functions and its X-ray transform.

All in One
Original Grayscale Image	Wave Front Set
X-ray transform	Wave Front Set
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.