Magnetic induction tomography via the monotonicity principle

Abstract

This contribution is focused on the nonlinear and ill-posed problem of reconstructing the electrical conductivity starting from the free response of a conductor in the magneto-quasi-stationary (MQS) limit. In this framework, a key role is played by the Monotonicity Principle, that is a monotone relation connecting the unknown material property to the (measured) free-response. The Monotonicity Principle is relevant to develop noniterative and real-time imaging methods. The Monotonicity Principle is a rather general principle found in many different physical problems. However, each physical/mathematical context requires the proper operator showing the MP to be identified. In turns, this calls for ad-hoc mathematical approaches tailored to the specific frameworks. In this paper we discuss a monotonic relationship between the electrical resistivity and the time constants of the free response for MQS systems. Numerical examples are provided to support the underlying theory.