A novel fast algorithm for electrical capacitance tomography (ECT) was presented.The minimum norm solution was improved according to the nature of the inverse problems of ECT, and the stability of the numerical solution for the improvement was proved via the singular value decomposition principle.Some equations for further improvement of the reconstructed image were deduced by numerical optimization.Numerical experiments indicated that the improvement was efficient and the time of image reconstruction was similar to that of linear back-projection (LBP), however, the quality of the reconstructed image is better than other image reconstruction algorithms such as LBP, Tikhonov and Landweber algorithm.
