Quantitative Object Reconstruction using Abel Transform X-ray Tomography and Mixed Variable Optimization

Abstract

This paper introduces a new approach to the problem of quantitatively reconstructing cylindrically symmetric objects from radiograph data obtained via x-ray tomography. Specifically, a mixed variable programming (MVP) problem is formulated, in which the variables of interest are the number and types of materials and the thickness of each concentric layer. The objective function is a measure of distance between one-dimensional radiograph data and a material property vector operated on by a forward projection based on the Abel transform. The mixed variable pattern search (MVPS) algorithm for linearly constrained MVP problems is applied to the problem by means of the NOMADm MATLABr software package. Numerical results are presented for several test configurations and show that, while there are difficulties yet to be overcome, the method appears to be very promising for solving this class of problems in practice.

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Document Details

Document Type
Technical Report
Publication Date
Feb 12, 2007
Accession Number
ADA464329

Entities

People

  • J. E. Dennis
  • Kevin R. O'reilly
  • Mark A. Abramson
  • Rachael L. Pingel
  • Thomas J. Asaki

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Detectors
  • Dielectrics
  • Geometry
  • Materials
  • Mathematics
  • Metals
  • Optimization
  • Ratings
  • Scattering
  • Test Sets
  • Three Dimensional
  • Tomography
  • X Rays

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Medical Imaging.
  • Operations Research