MRI-based electric properties tomography with a quasi-Newton approach

Abstract

Magnetic resonance electric properties tomography is a non-destructive imaging modality that maps the spatial distribution of the electrical conductivity and permittivity of the human body using standard clinical magnetic resonance imaging systems. From the magnetic field maps and the local form of the Maxwell equations, several schemes have been derived to provide direct approximated formulas but they suffer from instabilities. In this paper, we propose to address it as an inverse problem solved by a constrained optimization algorithm where we exploit the weak formulation of the electric Helmholtz equation and a Lagrangian approach. We derive the associated adjoint field equation and employ a quasi-Newton minimization scheme. We also take advantage of a regularisation strategy based on geometrical a priori information for defining large zones into which the electric parameters are known to be piece-wise constant.