Recent developments of a monotonicity imaging method for magnetic induction tomography in the small skin-depth regime

This paper is focused on the non-iterative (direct) imaging of conductive materials from magnetic induction tomography data. Specifically, the interest is on the imaging of surface-breaking defects in the so-called small skin-depth regime where (i) the skin depth is smaller than the relevant geometrical size of the problem and (ii) the displacement current is still negligible. Under these conditions the problem can be modeled by means of an elliptic PDE. Therefore, the inverse problem can be solved by means of the 'monotonicity imaging method', a fast non-iterative algorithm recently developed by the authors for solving inverse problems arising from elliptic PDEs as in the case of electrical resistance tomography, electrical capacitance tomography and low-frequency magnetic induction tomography (in the large skin-depth regime). Major contributions of this work are (i) an advancement of the inversion method and (ii) amethodology to systematically design the probe. Numerical examples prove the effectiveness of this near real-time imaging method.