Performance evaluation of an iterative image reconstruction algorithm with sensitivity matrix updating based on real measurements for electrical capacitance tomography

Abstract

Image reconstruction in electrical capacitance tomography requires a solution of an ill-posed inverse problem with an unknown measuring model which can be estimated during a reconstruction process. This paper presents a new version of a nonlinear iterative reconstruction similar to the Levenberg method. Only a few updates of the Jacobian are performed in contrast to modification every step in nonlinear iterative algorithms. A specialized numerical procedure was applied to speed up calculation of a sensitivity matrix. A step length factor together with a regularization parameter was used. A constraint for an estimated permittivity value was introduced. The L-curve method was applied to estimate the value of the regularization parameter. A proposed algorithm was evaluated on real objects and their numerical representations. A 16 electrode tomograph was used for real data acquisition. The elaborated algorithm achieves good quality of reconstructed images with reduced computation time.