Elimination of Nonpivotal Plane Images from X-Ray Motion Tomograms

A method for eliminating the contribution of nonpivotal plane images into a conventional X-ray motion tomogram is described. A set of tomograms, each focused on one of distinct parallel planes, are combined to form a blur-free tomogram. From the mathematical analysis of conventional tomography, it is found that the multisection tomography system reduces to a three-dimensional incomplete linear system with angularly limited frequency response. An iterative constrained reconstruction algorithm incorporating the object boundary constraint is used for reconstruction of a blur-free tomogram without a contribution from nonpivotal planes. Some computer simulations were made for verification of the algorithm. Although the algorithm accomplishes the three-dimensional reconstruction of volume rather than image restoration of a single slice plane, the optimal high-pass spatial filter applying to a single tomogram is derived on the way to solving the inverse problem of the multisection tomography system.