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arXiv · 2012.13950

The Monotonicity Principle for Magnetic Induction Tomography

Antonello Tamburrino·Gianpaolo Piscitelli·Zhengfang Zhou
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Abstract

The inverse problem treated in this article consists in reconstructing the electrical conductivity from the free response of the system in the magneto-quasi-stationary (MQS) limit. The MQS limit corresponds to a diffusion PDE. 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. MP is relevant as basis of noniterative and real-time imaging methods. Monotonicity Principles have been found in many different physical problems governed by PDEs of different nature. Despite its rather general nature, each different physical/mathematical context requires to discover the proper operator showing MP. For doing this, it is necessary to develop ad-hoc mathematical approaches tailored on the specific framework. In this article, we prove a monotonic relationship between the electrical resistivity and the time constants characterizing the free-response for MQS systems. The key result is the representation of the induced current density through a modal representation. The main result is based on the analysis of an elliptic eigenvalue problem, obtained from separation of variables.

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Antonello Tamburrino, Gianpaolo Piscitelli, Zhengfang Zhou. 2021-07-21. The Monotonicity Principle for Magnetic Induction Tomography. https://doi.org/10.1088/1361-6420%2Fac156c

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