The mathematical theory of CT came from J. Radon in 1917. It was declared that whole projection data sets were needed to reconstruct CT images. Therefor Limited CBCT was impossible under the theory of J. Radon.
In this paper I discover how to reconstruct Limited CBCT images under a new theory. This theory was shown that Limited CBCT images can be reconstructed, if the objects were high contrast such as teeth and bone, and the images did not require CT values. At the Same time, it was shown that Limited CBCT cannot reconstruct low contrast object such as soft tissue.
However, Limited CBCT is now very popular in dental practice. Because everyone knows that Limited CBCT had low radiation dose and high resolution.
I would like to introduce this mathematical theory and some episodes when I developed the Limited CBCT in 1990s.