Two-dimensional phase unwrapping

Many applications that rely on phase data, such as: synthetic aperture radar (SAR), magnetic resonance imaging (MRI) and interferometry involve solving the twodimensional phase unwrapping problem. The phase unwrapping problem has been tackled by a number of researchers who have attempted to solve it in many ways. This thesis examines the phase unwrapping problem from two perspectives. Firstly it develops two new techniques based upon the principles of Genetic Algorithms. Secondly it examines the reasons for failure of most of the common existing algorithms and proposes a new approach to ensuring the robustness of the phase unwrapping process. This new method can be used in conjunction of a number of algorithms including, but not limited to, the two Genetic Algorithm methods developed here. Some research effort has been devoted to solving the phase unwrapping problem using artificial intelligence methods. Recent developments in artificial intelligence have led to the creation of the Hybrid Genetic Algorithm approach which has not previously been applied to the phase unwrapping problem. Two hybrid genetic algorithm methods for solving the two dimensional phase unwrapping problem are proposed and developed in this thesis. The performance of these two algorithms is subsequently compared with several existing methods of phase unwrapping. The most robust existing phase unwrapping techniques use exhaustive computations and approximations, but these approaches contribute little towards understanding the cause of failure in the phase unwrapping process. This work undertakes a thorough investigation to the phase unwrapping problem especially with regard to the problem of residues. This investigation has identified a new feature in the wrapped phase data, which has been named the residue-vector. This residue-vector is generated by the presence of a residue, it has an orientation that points out towards the balancing residue of opposite polarity and it can be used to guide the manner in which branch-cuts are placed in phase unwrapping. Also, the residue-vector can be used for the determination of the weighting values used in different existing phase unwrapping methods such as minimum cost flow and least squares. In this work, the theoretical foundations of the residue-vector method are presented and a residue-vector extraction method is developed and implemented. This technique is then demonstrated both as an unwrapping tool and as an objective method for determining a quality map, using only the data in the wrapped phase map itself. Finally a general comparison is made between the residue-vector map and other existing quality map generation methods. i Two-Dimensional Phase Unwrapping Acknowledgement Acknowledgement It has been an honour and a privilege to be associated with Professor Michael Lalor and Professor David Burton for carrying out the research work towards my PhD degree. I have greatly benefited from their deep insight and expertise into the subject. With their professional guidance, invaluable advice, patience, constant support and encouragement, throughout the different stages of the project I was able to publish my work presented in this thesis in two international journal papers and to be recognized in the field of research by many researchers. Therefore I would like to take this opportunity to express my gratitude and sincere thanks to them. Also, I acknowledge valuable time spent by Dr. Francis Lilley in helping me correct and edit my papers I have published. I would like to express my thanks and appreciation especially for his quick response for help. I would like to thank my supervisor, Dr. Munther Gdeisat, for his help, time, encouragement, advice and motivation that he provided me through the period of my PhD degree. Besides, learning his engineering techniques and understanding the project. Again, I would like to express my deep thanks and gratitude. On a more personal note, I must thank my parent for their endless support throughout my studies. Without their constant assurance and assistance, completion of this project would have not been possible. Their enthusiasm, drive, strength of character, tenacity and determination have inspired me to carry out this research work. And as a sign of my love, gratitude and affection I dedicate this work to them. I want to thank my wife for her support and motivation in the completion of my PhD degree.