Affiliations: [a] Department of Electrical and Information Engineering, University of Cassino and Southern Lazio, Cassino, Italy | [b] Department of Electrical and Information Engineering, University of Cassino and Southern Lazio, Cassino, Italy | [c] Dipartimento di Scienze Economiche, Giuridiche, Informatiche e Motorie, Università degli Studi di Napoli Parthenope, Naples, Italy | [d] Department of Electrical and Information Engineering, University of Cassino and Southern Lazio, Cassino, Italy | [e] Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA
Correspondence:
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Corresponding author: Vincenzo Mottola, Department of Electrical and Information Engineering, University of Cassino and Southern Lazio, Cassino, Italy. E-mail: vincenzo.mottola@unicas.it
Abstract: In this paper we present a first non-iterative imaging method for nonlinear materials, based on Monotonicity Principle. Specifically, we deal with the inverse obstacle problem, where the aim is to retrieve a nonlinear anomaly embedded in linear known background. The Monotonicity Principle (MP) is a general property for various class of PDEs, that has recently generalized to nonlinear elliptic PDEs. Basically, it states a monotone relation between the point-wise value of the unknown material property and the boundary measurements. It is at the foundation of a class of non-iterative imaging methods, characterized by a very low execution time that makes them ideal candidates for real-time applications. In this work, we develop an inversion method that overcomes some of the peculiar difficulties in practical application of MP to imaging of nonlinear materials, preserving the feasibility for real-time applications. For the sake of clarity, we focus on a specific application, i.e. the Magnetostatic Permeability Tomography where the goal is retrieving the unknown (nonlinear) permeability by boundary measurements in DC operations. This choice is motivated by applications in the inspection of boxes and containers for security. Reconstructions from simulated data prove the effectiveness of the presented method.
