A comparative analysis between different inversion algorithms for process tomographic measurements

In measurements science and its technological application most of the measurement methods are indirect. In order to measure the unknown physical quantity y we have, to develop a forward model which relates this quantities to another one x directly measurable: x→y. Often the measurement model available is of the opposite nature, i.e. y→x. It is thus necessary to invert the available model: this operation in some cases can lead to an unacceptable level of uncertainty in the results. The inversion procedure requires regularization techniques in order to limit the uncertainty affecting the indirect measurements. This operation can be accomplished adopting different algorithms proposed by various authors. This paper shows a comparison of some algorithms for processing measured data using ill-conditioned inverse models employed for determining the distribution of indirectly measured quantities. They all perform Tikhonov regularization. The comparison is performed analyzing their metrological performances on the basis of two application tests, one linear and one non linear.