Optimization of the set of path-rays in linear tomography

In this work a new formalization of selecting the optimal set of path-rays problem in linear tomography is presented. In particular the problem of selecting the optimal set of path-rays is formalized as a problem of selecting a sub-matrix of a matrix with certain spectral properties, which is known to be an NP-hard problem. New criteria of optimality of the set of path-rays are introduced, and an optimization algorithm is proposed to deal with the combinatory search problem. The obtained results are compared to those of existing approximation algorithms. Numerical results show that the optimal solutions yielded by the proposed optimization algorithm, outperform existing algorithms in terms of conditioning of the tomography linear equations system.