12 - Direct image reconstruction in electrical tomography and its applications

Abstract

Electrical tomography (ET) recovers the cross-sectional material distribution of the region of interest (ROI), in the form of reconstructed images from measured capacitances on the boundary. However, the “soft” field nature of the electromagnetic field hinders the image reconstruction in the tomography. Usually, most of the reconstruction algorithms of ET used the sensitivity or Jacobian matrix to achieve the retrieval of the material distributions. For these algorithms, the conductivity or permittivity perturbations for the whole domain must be reconstructed simultaneously. In the chapter, several direct algorithms, e.g., Calderon's method, dbar method and factorization method, etc., for ET are presented. Direct methods reconstruct only a part of the ROI without information of the other parts. Also, typical PID controller was introduced to improve the image quality in the reconstruction. Moreover, these methods can be easily generalized to the case of sensors of noncircular cross-sections by using conformal transformations. Reconstructed images in different cases of phantoms are obtained to verify the effectiveness of these methods.