Quantitative Object Reconstruction Using Abel Transform X-Ray Tomography and Mixed Variable Optimization

This paper introduces a new approach to the problem of quantitative reconstruction of an object from few radiographic views. A mixed variable programming problem is formulated in which the variables of interest are the number and types of materials and geometric parameters. To demonstrate the technique, we considered the problem of reconstructing cylindrically symmetric objects of multiple layers from a single radiograph. The mixed variable pattern search algorithm for linearly constrained problems was applied by means of the NOMADm MATLAB software package. Numerical results are presented for several test configurations and show that, while there are difficulties yet to be overcome, the method is promising for solving this class of problems.