Investigation of relaxation factor in landweber iterative algorithm for electrical capacitance tomography

It is crucial to select a suitable relaxation factor in iterative image reconstruction algorithms (e.g. Landweber iterative algorithm) for electrical capacitance tomography (ECT) because it affects the convergence. By simulation, it is found notably that the relaxation factor should be selected adaptively according to the sensor structure (e.g. the number of electrodes) and the permittivity distribution in capacitance measurements. With different number of electrodes and four typical permittivity distributions, the relaxation factor and the related convergence are investigated in consideration of the change in relative image error. It is shown that the relaxation factor can be chosen based on the upper boundary of all relaxation factors. The conclusions in this paper can be used for practical industrial processes, regarding the adaptive selection of relaxation factor and the number of iterations needed.