Adaptive selection of relaxation factor in Landweber iterative algorithm

It is crucial to select a suitable relaxation factor in Landweber iterative algorithm for electrical capacitance tomography, because it affects the convergence and convergence rate. Previous study shows that the relaxation factor should be selected adaptively according to the sensor structure (e.g., the number of electrodes), permittivity distribution, and noise level in capacitance data. 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 and relative capacitance residual. By adding noises with different levels to noise-free data, their influences on the selection of relaxation factor and convergence are characterized. For a typical permittivity distribution, the corresponding relaxation factor is selected based on the upper bound of all relaxation factors, which are determined by a sensor design. The performance of Landweber algorithm with an adaptively selected relaxation factor is compared with constant relaxation factors and updated relaxation factor, showing that the proposed method can ensure convergence with less computation time than other relaxation factors.