Research On Two-dimensional Phase Unwrapping In MRI

In magnetic resonance imaging (MRI), the complex signal contains both the magnitude and phase parts. Usually the magnitude of the MRI signal has been mainly considered. However, the phase of MRI signal offers very important information on the velocity of the moving spins, the main Bo field inhomogeneity, the magnetic susceptibility variations, etc. So the phase can be used to estimate the main B0field inhomogeneity and obtain clinically relevant physiological parameters.when extracting the phase from a measured complex MR dataset through some mathematical operation, the result is typically wrapped into the principal interval of (-π,π] radians, producing the wrapped phase. The process of estimating the true phase from the wrapped phase is called phase unwrapping. Because of the presence of the noise, undersampling and/or object discontinuities, phase unwrapping becomes intractable and nontrivial. In the literature, there are quite a few existing phase unwrapping algorithms.In this thesis, three two-dimensional (2D) phase unwrapping methods were proposed. Both simulated and MR data were used to evaluate these algorithms’ performances.(1) A new branch-cut method based on discrete particle swarm optimization (dPSO) algorithm was proposed to solve the phase unwrapping problem of MR data. In this method, all the residues were first grouped by dividing the phase image into sub-regions. Then dPSO was performed region by region to match the opposite polarity residues which were connected by branch cuts afterward. Finally, flood-fill method was used to unwrap phases avoiding these branch cuts. Compared with conventionally used branch-cut phase unwrapping algorithms, the dPSO algorithm is rather robust and effective.(2) A direct-solver-based weighted minimum Lp-norm algorithm was proposed for MRI phase unwrapping. First, the algorithm converted the weighted minimum-Lp-norm objective function for phase unwrapping into a linear system of equations whose system (coefficient) matrix was a large, symmetric one. Then, the coefficient-matrix was represented in the sparse structure. Finally, standard direct solvers were employed to solve this linear system. The results demonstrate that the proposed algorithm is reliable and robust.(3) A mask-based region growing approach was proposed for MRI phase unwrapping. The residues were first connected by zero-value pixels that were then served as mask. And the mask and the original quality map were combined into a new quality map. Guided by the new quality map, unwrapping was carried out within multiple regions. At last, the regions were merged by adjusting the offset between one another. The results show the advantage of the proposed approach over the recent region-growing phase unwrapping method (PHUN) in accuracy.