Direct Image Reconstruction for Electrical Capacitance Tomography Using Shortcut D-Bar Method

In this paper, the shortcut D-bar method is introduced to electrical capacitance tomography to directly reconstruct the permittivity distribution within the region of interest. The method reveals the analytic relationship between the permittivity distribution and the Dirichlet-to-Neumann (DN) map. The DN map can be directly estimated with measured capacitances. However, the direct estimate of the DN map is inaccurate in the cases of small electrode numbers. To better adapt the method to real applications of small electrode numbers, the original shortcut D-bar method is modified by splitting estimation of the DN map into the analytical expression of a homogeneous background and the estimation of the other variation part. Comparisons are made among the original, modified shortcut D-bar methods, and the classical Landweber iteration method through simulation and experiment, respectively. Results confirm the improved tomographic imaging quality by using the modified shortcut D-bar method.