Towards improved metal detection of multiple inhomogeneous conducting objects using magnetic polarizability tensors

Abstract: Locating and identifying hidden conducting objects has a range of important applications including searching for buried treasure, identifying landmines and in the early detection of concealed terrorist threats. The presence of multiple objects is common and includes benign situations, such as coins and keys accidentally left in a pocket during a security search or a treasure hunter becoming lucky and discovering a hoard of Roman coins, as well as threat situations, where the risks need to be clearly identified from the background clutter. Furthermore, objects are also often inhomogeneous and made up of several different metals. For instance, the barrel of a gun is invariably steel while the frame could be a lighter alloy, jacketed bullets have a lead shot and a brass jacket and modern coins often consist of a cheaper metal encased in nickel or brass alloy. Thus, in practical metal detection applications, it is important to be able to characterise both multiple objects and inhomogeneous objects.

Traditional approaches to the metal detection problem involve determining the conductivity and permeability distributions in the eddy current approximation of Maxwell’s equations and lead to an ill-posed inverse problem. On the other hand, practical engineering solutions in hand held metal detectors use simple thresholding and are not able to discriminate between small objects close to the surface and larger objects buried deeper underground.

In this talk, an alternative approach in which prior information about the form of the conducting permeable object has been introduced will be discussed. This allows the perturbed magnetic field, due to the presence of a conducting permeable object, to be described in the form of an asymptotic expansion as the object size tends to zero. The asymptotic expansion separates the object’s position from its shape and material description offering considerable advantages in case of isolated objects. Our previous result focused on a single homogenous object, which was described using a rank 2 magnetic polarizability tensor (MPT). Recently, we have extended the asymptotic expansion to characterise multiple inhomogeneous objects, including objects that are closely spaced, in terms of MPTs. The coefficients of each MPT can be computed by solving a vector valued transmission problem numerically using finite elements for each object.

The talk will explore the interesting properties exhibited by MPTs for different types of objects. It will also describe how the eigenvalues of the MPTs for candidate target objects can form a dictionary for object classification. Initial investigations using a simple dictionary matching algorithm for object identification will also be included and the scope for using machine learning approaches will also be discussed.

Biography: Dr Paul Ledger is an Associate Professor in the College of Engineering at Swansea University. He has worked at Swansea University since 2006 starting as a Lecturer before being promoted in 2013. His research is focused on addressing important challenges in public safety and security as well as improving medical imaging technologies. He works at the interface of Applied Mathematics, Engineering and Computational Science. His recent research activities have focused on developing new mathematical and computational techniques for characterising and locating metallic (threat) objects for safety and security applications. In this field He enjos collaborating with Professor Lionheart from The University of Manchester and some of our recent work has been supported by EPSRC. He is also very active in the simulation of complex coupled problems such as understanding the mechanical vibrations and acoustic noise produced by MRI scanners. In this field he is working together with Dr Gil from Swansea University and his work is supported by EPSRC and Siemens Magnet Technology.