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

This paper introduces a new approach to the problem of quantitatively reconstructing cylindrically symmetric objects from radiograph data obtained via x-ray tomography. Specif-ically, 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 trans-form. The mixed variable pattern search (MVPS) algorithm for linearly constrained MVP problems is applied to the problem by means of the NOMADm MATLAB r 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. Key words: Mixed variable optimization, derivative-free optimization, mesh adap-tive direct search (MADS) algorithms, x-ray tomography, Abel transforms AMS 65K05, 65R32, 65R10, 90C30, 90C56