Eddy Current Tomography

In eddy current tomography, the conductivity profile of conductive materials is reconstructed through the inversion of eddy current data (ECT). The state of the art of imaging methods in ECT data inversion is represented by iterative methods, the drawbacks of which are their high computational cost and the risk of becoming trapped in false solutions (local minima). In this chapter, we discuss the “Monotonicity Principle Method,” a fast non-iterative approach recently developed for elliptic problems (such as electrical resistance tomography) and then extended to parabolic problems (such as eddy current tomography) and hyperbolic problems (such as microwave tomography). This chapter discusses the main features of the Monotonicity Principle in eddy current testing. Specifically, section “Monotonicity Principle for Eddy Current Imaging in the Large Skin-Depth Regime” discusses the Monotonicity Principle for eddy current testing in the “large” skin-depth regime, then section “Imaging Method” introduces the related imaging method (Monotonicity Principle Imaging Method, MPIM), and section “Monotonicity Principle for Eddy Currents in Other Settings” introduces other setting where Monotonicity Principle holds and MPIM can be applied.