Reconstruction Algorithms for Permittivity and Conductivity Imaging

Bill Lionheart

Department of Mathematics, UMIST, UK Email: bill.lionheart@umist.ac.uk

ABSTRACT

Linear reconstruction algorithms are reviewed using assumed covariance matrices for the conductivity and data and the formulation of Tikhonov regularization using the singular value decomposition (SVD) with covariance norms. It is shown how iterative reconstruction algorithms, such as Landweber and conjugate gradient, can be used for regularization and analysed in terms of the SVD, and implemented directly for a one-step Newton's method. Where there are known inequality constraints, such as upper and lower bounds, these can be incorporated in iterative methods and have a stabilizing effect on reconstructions.

Keywords Reconstruction algorithms, electrical imaging, ECT, ERT, regularization