The first part of this work reviews the algebraic matricial approach to transport data inversion. It works for the convection–diffusion transport equation used for periodic signals and provides a formally exact solution, as well as a quantitative assessment of error bars. The standard methods of reconstruction infer the diffusivity D and pinch V by matching experimental data against those simulated by transport codes. These methods do not warrant the validity of either the underlying models of transport, or of the reconstructed D(r) and V(r), even when the results look reasonable. However, the adoption of automated global search algorithms based upon genetic algorithms is bound to greatly increase the probability of finding optimal solutions.