The early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterisation information. The magnetic polarizability tensor (MPT) offers an economical characterisation of metallic objects that can be computed for different threat and non-threat objects and has an established theoretical background, which shows that the induced voltage is a function of the hidden object's MPT coefficients. In this article, we describe the additional characterisation information that measurements of the induced voltage over a range of frequencies offer compared with measurements at a single frequency. We call such object characterisations its MPT spectral signature. Then, we present a series of alternative rotational invariants for the purpose of classifying hidden objects using MPT spectral signatures. Finally, we include examples of computed MPT spectral signature characterisations of realistic threat and non-threat objects that can be used to train machine learning algorithms for classification purposes.

The identification of hidden conducting permeable objects from measurements of the perturbed magnetic field taken over a range of low frequencies is important in metal detection. Applications include identifying threat items in security screening at transport hubs, location of unexploded ordnance, and antipersonnel landmines in areas of former conflict, searching for items of archeological significance and recycling of valuable metals. The solution of the inverse problem, or more generally locating and classifying objects, has attracted considerable attention recently using polarizability tensors. The magnetic polarizability tensor (MPT) provides a characterization of a conducting permeable object using a small number of coefficients, has an explicit formula for the calculation of their coefficients, and a well understood frequency behavior, which we call its spectral signature. However, to compute such signatures, and build a library of them for object classification, requires the repeated solution of a transmission problem, which is typically accomplished approximately using a finite element discretization. To reduce the computational cost, we propose an efficient reduced order model (ROM) that further reduces the problem using a proper orthogonal decomposition for the rapid computation of MPT spectral signatures. Our ROM benefits from a posteriori error estimates of the accuracy of the predicted MPT coefficients with respect to those obtained with finite element solutions. These estimates can be computed cheaply during the online stage of the ROM allowing the ROM prediction to be certified. To further increase the efficiency of the computation of the MPT spectral signature, we provide scaling results, which enable an immediate calculation of the signature under changes in the object size or conductivity. We illustrate our approach by application to a range of homogenous and inhomogeneous conducting permeable objects.

The early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterization information. The magnetic polarizability tensor (MPT) offers an economical characterization of metallic objects and its spectral signature provides additional object characterization information. The MPT spectral signature can be determined from measurements of the induced voltage over a range of frequencies in a metal signature for a hidden object. With classification in mind, it can also be computed in advance for different threat and non-threat objects. In this article, we evaluate the performance of probabilistic and non-probabilistic machine learning algorithms, trained using a dictionary of computed MPT spectral signatures, to classify objects for metal detection. We discuss the importance of using appropriate features and selecting an appropriate algorithm depending on the classification problem being solved, and we present numerical results for a range of practically motivated metal detection classification problems.

The early detection of terrorist threats, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterisation information. The magnetic polarizability tensor (MPT) offers an economical characterisation of metallic objects that can be computed for different threat and non-threat objects and has an established theoretical background, which shows that the induced voltage is a function of the hidden object's MPT coefficients. In this paper, we describe the additional characterisation information that measurements of the induced voltage over a range of frequencies offer compared to measurements at a single frequency. We call such object characterisations its MPT spectral signature. Then, we present a series of alternative rotational invariants for the purpose of classifying hidden objects using MPT spectral signatures. Finally, we include examples of computed MPT spectral signature characterisations of realistic threat and non-threat objects that can be used to train machine learning algorithms for classification purposes.

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