Overview

Researchers at the Los Alamos National Laboratory (LANL) are interested in quantitatively reconstructing an object using Abel transform x-ray tomography. Specifically, they obtain a radiograph by x-raying an object and attempt to quantitatively determine the number and types of materials and the thicknesses of each material layer. Their current methodologies either fail to provide a quantitative description of the object or are generally too slow to be useful in practice. As an alternative, the problem is modeled here as a mixed variable programming (MVP) problem, in which some variables are nonnumeric and for which no derivative information is available. The generalized pattern search (GPS) algorithm for linearly constrained MVP problems is applied to the x-ray tomography problem, by means of the NOMADm MATLABr software package. Numerical results are provided for several test configurations of cylindrically symmetrical objects and show that, while there are difficulties to be overcome by researchers at LANL, this method is promising for solving x-ray tomography object reconstruction problems in practice. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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