Humanitarian clearance of minefields is most often carried out by hand, conventionally using a a metal detector and a probe. Detection is a very slow process, as every piece of detected metal must treated as if it were a landmine and carefully probed and excavated, while many of them are not. The process can be safely sped up by use of GroundPenetrating Radar (GPR) to image the subsurface, to verify metal detection results and safely ignore any objects which could not possibly be a landmine. In this thesis, we explore the possibility of using Full Wave Inversion (FWI) to improve GPR imaging for landmine detection. Posing the imaging task as FWI means solving the largescale, nonlinear and illposed optimisation problem of determining the physical parameters of the subsurface (such as electrical permittivity) which would best reproduce the data. This thesis begins by giving an overview of all the mathematical and implementational aspects of FWI, so as to provide an informative text for both mathematicians (perhaps already familiar with other inverse problems) wanting to contribute to the mine detection problem, as well as a wider engineering audience (perhaps already working on GPR or mine detection) interested in the mathematical study of inverse problems and FWI.We present the first numerical 3D FWI results for GPR, and consider only surface measurements from smallscale arrays as these are suitable for our application. The FWI problem requires an accurate forward model to simulate GPR data, for which we use a hybrid finiteelement boundaryintegral solver utilising first order curlconforming N\'{e}d\'{e}lec (edge) elements. We present a novel `line search' type algorithm which prioritises inversion of some target parameters in a region of interest (ROI), with the update outside of the area defined implicitly as a function of the target parameters. This is particularly applicable to the mine detection problem, in which we wish to know more about some detected metallic objects, but are not interested in the surrounding medium. We may need to resolve the surrounding area though, in order to account for the target being obscured and multiple scattering in a highly cluttered subsurface.We focus particularly on spatial sensitivity of the inverse problem, using both a singular value decomposition to analyse the Jacobian matrix, as well as an asymptotic expansion involving polarization tensors describing the perturbation of electric field due to small objects. The latter allows us to extend the current theory of sensitivity in for acoustic FWI, based on the Born approximation, to better understand how polarization plays a role in the 3D electromagnetic inverse problem. Based on this asymptotic approximation, we derive a novel approximation to the diagonals of the Hessian matrix which can be used to precondition the GPR FWI problem.
Date of Award  1 Aug 2016 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  William Lionheart (Supervisor) & Robin Marshall (Supervisor) 

 RWG
 Scattering
 FEBI
 FEBI
 Boundary integral
 BEM
 Inverse scattering
 edge elements
 FEM
 Regularization
 Sensitivity
 TV
 Optimisation
 lBFGS
 Preconditioning
 Spatial sensitivity
 Shape sensitivity
 Hessian
 Nuisance parameters
 Total variation
 Nedelec elements
 FWI
 Surface equivalence
 ROI
 Inverse problems
 Illposed
 Nonlinear
 Imaging
 Fullwave inversion
 Fullwaveform inversion
 SVD
 polarization tensor
 Finite element
 polarizability tensor
 landmine detection
 Ground penetrating radar
 GPR
 3D
 Helmholtz equation
 Electromagnetics
 Maxwell's equations
 Computational electromagnetics
 Vector wave equation
 asymptotic
 Region of interest
Better Imaging for Landmine Detection: An exploration of 3D fullwave inversion for groundpenetrating radar
Watson, F. (Author). 1 Aug 2016
Student thesis: Phd