Noise limitations on the recovery of average values of velocity profiles in pipelines by simple imaging systems

This letter deals with a recently proposed two-step algorithm for the reconstruction of dielectric and velocity profiles of axially moving cylinders. In particular, the aim of the present work is to investigate the limitations and capabilities in reconstructing the velocity profile. By considering a best-case scenario, it is shown that, although the algorithm should be able to work even in the presence of flows with very small axial velocity values, reliable results can only be obtained when the axial speed is larger than a lower bound. This bound is shown to be an intrinsic limitation of the algorithm which is only related to the cross-polarization isolation of the measurement system. Other simulations, based on worst-case scenarios, confirm that such a bound is independent of the type of flow considered, of the configuration of the measurement system, and of the errors coming from the step devoted to the reconstruction of the dielectric profile. Finally, the same simulations show that the algorithm is reliable in a wide range of speed values, provided sensors with large cross-polarization isolations are exploited.