A new method based on discrete particle swarm optimization (dPSO) algorithm is proposed to solve the branch-cut phase unwrapping problem of MRI data. In this method, the optimal order of matching the positive residues with the negative residues is first identified by the dPSO algorithm, then the branch cuts are placed to join each pair of the opposite polarity residues, and in the last step phases are unwrapped by flood-fill algorithm. The performance of the proposed algorithm was tested on both simulated phase image and MRI wrapped phase data sets. The results demonstrated that, compared with conventionally used branch-cut phase unwrapping algorithms, the dPSO algorithm is rather robust and effective. 1. Introduction 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, and can also be used to deduce useful information about the main field inhomogeneity and the magnetic susceptibility variations . In MRI, the phase information is usually obtained from a complex MRI dataset through some mathematical operations, and the value always lies in the principal interval of , consequently producing a wrapped phase . This relationship can be described by , where is an integer and defines a wrapping operator that forces all values of its argument into the range by adding or subtracting an integral multiple of radians from its argument. Phase unwrapping is the process of estimating the true phase from the wrapped phase . As an important tool, it can not only be used for the three-point Dixon water and fat separation, but also be applied to increase the dynamic range of phase contrast MR velocity measurements . If the true phase gradients (i.e., the differences of ) between contiguous pixels are less than π radians in magnitude in the entire space, the true phase can be unwrapped in a straightforward manner by just integrating the wrapped phase gradients . However, the presence of the noise, undersampling, and/or object discontinuities often makes this condition unavailable. Therefore, the problem of phase unwrapping becomes complex in practice and difficult to solve, although significant amount of research effort has been devoted to date. In the literature, there are quite a few existing phase unwrapping algorithms , which can be grouped into two categories: path-following and minimum-norm methods . The branch-cut phase unwrapping
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