Magnetic resonance imaging (MRI) is one of the most outstanding developments in medical diagnosis in recent decades. It is used in a wide range of clinical imaging applications, and is particularly effective for producing high quality images of soft tissues. It should therefore be well-suited to evaluating complications arising in patients with orthopaedic metal implants which are considered safe for MRI scanning. However, the presence of the metal produces large variations in the magnetic field, and the resulting images have significant artifacts.

Performing accurate fat suppression near metal implants remains an unsolved challenge in MRI. The ability to use multipoint fat suppression techniques close to metal would be greatly beneficial, as it would allow for easier diagnosis of certain soft tissue complications through contrast-enhanced imaging. To succeed, multipoint techniques require a robust and accurate method for estimating the magnetic field variation induced by the metal. Existing methods tend to fail near the boundary of the metal where the field is rapidly varying. This thesis explores new methods for estimating the phase shift due to the magnetic field variation in the three-point Dixon technique near metal. The problem of phase unwrapping in regions where the phase varies rapidly is investigated. Magnetic field variation simulations are used throughout for developing and assessing these new methods.

The most significant contribution presented is the development and evaluation of the Phase Onion Peeling (POP) algorithm. POP is a novel approach to phase estimation in the three-point Dixon technique. POP estimates the phase across a two-dimensional slice using a set of closed paths which enclose the implant boundary. The phase is first estimated at the outer edges of the slice. The method incrementally works inwards along a set of adjacent paths, finishing at the boundary of the implant. The phase along each path is represented by a Fourier series, and the coefficients for each path are estimated by minimising an objective function. The main advantage of POP over existing techniques is that the phase unwrapping problem is converted to one of parameter estimation. POP was tested on data acquired from three phantoms and seven human participants, with results presented and evaluated. POP is shown to have superior performance compared to existing phase unwrapping methods and better or comparable performance to the IDEAL reconstruction method.

This thesis also presents a number of other contributions: a detailed assessment of the performance of existing phase unwrapping methods in the vicinity of metal; an analysis of existing iterative techniques in regions of rapid magnetic field variation; a proposed extension to POP to use a different objective function form; an exploration into using POP in conjunction with the matching pursuit algorithm; and a description of three phase estimation methods developed before POP.