Deblurring and Three-Dimensional Reconstruction from Multiple Linear-Tomograms

Abstract

The image of the tomogram obtained by a conventional x-ray tomographic machine is degraded by the superposition of motion-blurred images of nonpivotal planes. We introduce a method to eliminate these blurred images from a tomogram. In this method a set of tomograms, each focused on one of a set of parallel planes, are combined to form a three-dimensional reconstruction of blur-free tomograms. This approach is equivalent to the inversion of a linear system. By a mathematical analysis of linear-motion tomography, we found that linear-motion tomography is restricted to angularly-limited frequency information. An iterative matrix inversion algorithm with the constraints of nonnegativity and finite-extent is applied to the reconstruction of the plane of interest from a set of tomograms.