Wavelet preconditioning for EIT

Abstract

In this paper the forward problem of Electrical Impedance Tomography (EIT) is considered. To achieve a flexible treatment of boundaries, the original two-dimensional domain is extended to a simple square one and essential boundary conditions are imposed by means of Lagrange multipliers, resulting in a saddle point system. For discretisation, we employ a biorthogonal B-Spline wavelet basis for which it can be shown that in the suggested forward EIT formulation the condition number of the system matrix is asymptotically uniformly bounded, and therefore iterative solvers converge with a speed independent of the discretisation level.