Tomographic reconstructions from incomplete data-numerical inversion of the exterior Radon transform

X-rays passing through the beating heart or bone can create error in standard computer tomographic scans of the organs around these regions. Often doctors are interested in imaging only the organs surrounded in these regions, not the regions themselves. The author's algorithm reconstructs the organs around the heart or metal without using the X-rays that create the error. Reconstructions of mathematical phantoms using this algorithm are given, and a description of the completed algorithm is presented. A mathematical explanation is given for the difficulties inherent in any tomography problem with incomplete data. It predicts weaknesses inherent in all reconstruction algorithms that use incomplete data.