All Title Author
Keywords Abstract


A New Particle Swarm Optimization-Based Method for Phase Unwrapping of MRI Data

DOI: 10.1155/2012/475745

Full-Text   Cite this paper   Add to My Lib

Abstract:

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 [1]. 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 [2]. 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 [3]. 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 [4], which can be grouped into two categories: path-following and minimum-norm methods [5]. The branch-cut phase unwrapping

References

[1]  I. R. Young and G. M. Bydder, “Phase imaging,” in Magnetic Resonance Imaging, D. D. Stark and W. G. Bradley, Eds., Mosby Year Book, St. Louis, Mo, USA, 2nd edition, 1992.
[2]  J. Rydell, et al., “Phase sensitive reconstruction for water/fat separation in MR imaging using inverse gradient,” in Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI '07), Brisbane, Australia, October 2007.
[3]  K. Itoh, “Analysis of the phase unwrapping problem,” Applied Optics, vol. 21, no. 14, article 2470, p. 2470, 1982.
[4]  S. A. Karout, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Two-dimensional phase unwrapping using a hybrid genetic algorithm,” Applied Optics, vol. 46, no. 5, pp. 730–743, 2007.
[5]  D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software, John Wiley & Sons, New York, NY, USA, 1998.
[6]  R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Science, vol. 23, no. 4, pp. 713–720, 1988.
[7]  R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Applied Optics, vol. 34, no. 5, pp. 781–789, 1995.
[8]  J. R. Buckland, J. M. Huntley, and J. M. Turner, “Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm,” Applied Optics, vol. 34, no. 23, pp. 5100–5108, 1995.
[9]  J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948, December 1995.
[10]  Y. Shi and R. Eberhart, “Modified particle swarm optimizer,” in Proceedings of the 1998 IEEE International Conference on Evolutionary Computation (ICEC '98), pp. 1945–1950, May 1998.
[11]  N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 9, no. 1, pp. 62–66, 1979.
[12]  C. Wang, J. Zhang, J. Yang, C. Hu, and J. Liu, “A modified particle swarm optimization algorithm and its application for solving traveling salesman problem,” in Proceedings of the International Conference on Neural Networks and Brain Proceedings (ICNNB '05), pp. 689–694, October 2005.
[13]  M. Clerc, “Discrete particle swarm optimization,” 2000, http://clerc.maurice.free.fr/pso/pso_tsp/Discrete_PSO_TSP.htm.
[14]  K. P. Wang, L. Huang, C. G. Zhou, and W. Pang, “Particle swarm optimization for traveling salesman problem,” in Proceedings of the International Conference on Machine Learning and Cybernetics, pp. 1583–1585, November 2003.
[15]  Wikipedia, “Flood fill,” http://en.wikipedia.org/wiki/Flood_fill.
[16]  K. Chen, J. Xi, Y. Yu, and J. F. Chicharo, “Fast quality-guided flood-fill phase unwrapping algorithm for three-dimensional fringe pattern profilometry,” in Optical Metrology and Inspection for Industrial Applications, vol. 7855, October 2010.
[17]  B. Spottiswoode, “2D phase unwrapping algorithms,” http://www.mathworks.com/matlabcentral/fileexchange/22504.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal