In X-ray medical imaging,the promotion of 3D display techniques imposed to improve the spatial and temporal resolution of 3D acquisition-reconstruction devices. One solution is to use a 2D X-ray detector. For one source position,the attenuation measurement of the diverging X-ray beams provides a radiography. The source trajectory defines a set of acquisitions. In terms of illposed problems, we state that a circular trajectory centred on the area to reconstruct can be a good one, provided the source remains far enough from the object. We propose a direct reconstruction algorithm based on an approximated evaluation of the 3D Radon Transform and on the use of its inversion formula. We present the numerical foundations of such a transform method.
"Description Of A 3D Reconstruction Algorithm For Diverging X-Ray Beams", Proc. SPIE 0602, Biostereometrics '85, (7 July 1986); doi: 10.1117/12.956297; https://doi.org/10.1117/12.956297