Adjoint Formulations in Impedance Imaging

N Polydorides and W R B Lionheart

Dept. of Mathematics, UMIST, PO Box 88, Manchester, UK. Nicholas.Polydorides@umist.ac.uk

ABSTRACT

Most reconstruction algorithms in electrical impedance tomography (EIT, ERT and ECT) are known to suffer from the computational costs of calculating the Jacobian (also known as sensitivity matrix). In this paper we review and slightly modify the adjoint fields technique already widely used in electromagnetic imaging, diffuse optical and ultrasound tomography, which enables the reconstruction of nonlinear solutions without the explicit calculation of the Jacobian. This has enormous computational advantages in the efficiency of image reconstruction. Here we address the complex isotropic EIT problem.

Keywords Adjoint operator, electrical impedance tomography, computational efficiency.