关键词: 电容层析成像, 图像重建, 不适定反问题, Tikhonov正则化, 最小坡度, L-曲线

Abstract: Image reconstruction for electrical capacitance tomography is an inverse problem and is often ill posed. A new solution is proposed to the ill-posed inverse problem, i.e., choosing the Tikhonov regularization parameter within the minimum-slope curve segment. However, in the capacitance measurement data are perturbed, the sensitivities of some regularized solution to such ill-posed are lower than other solutions. For this reason, in the new solution a definitive criterion is taken to choose one of those insensitive regularized solution and a regularization parameter corresponding to the solution chosen is taken as the optimal value. Simulation tests of capacitance data measurement with noise were conducted and two typical permittivity distributions to compare the two results of image reconstruction to which the regularization parameter was calculated by choosing it within the minimum-slope curve segment and by the prevailing L-curve approach. It is shown that the effect of the image reconstruction by the former is better than by the latter.