Image reconstruction of electrical capacitance tomography (ECT) is a typical inverse problem owing to non-linearity and ill-posedness. At the same time, progress towards the solution of this kind of problem has been made at good speed as a branch of mathematics in the past three decades. In this paper, most of the regularization tools developed for the inverse problem are applied to the reconstruction of various simulated images by ECT. The results show promise for ECT image reconstruction by regularization methods. The non-linearity of the sensitivity matrix seems to be the major problem.