Magnetic Resonance Imaging
Volume 27, Issue 9 , Pages 1293-1301 , November 2009

Unwrapping magnetic resonance phase maps with Chebyshev polynomials

  • Jason Langley
    • ,
  • Qun Zhao

      Affiliations

    • Corresponding Author InformationCorresponding author. Department of Physics and Astronomy, The University of Georgia, Athens, GA, USA.

Received 18 February 2009 ,Revised 14 April 2009 ,Accepted 7 May 2009.

References 

  1. Poncelet BP, Wedeen VJ, Weisskoff RM, Cohen MS. Brain parenchyma motion: measurement with cine echo-planar MR imaging. Radiology. 1992;185:645–651
  2. Cusack R, Papadakis N. New robust 3-D phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images. NeuroImage. 2002;16:754–764
  3. Guo JY, Kholmovski EG, Zhang L, Parker DL. Evaluation of motion effects on parallel MR imaging with precalibration. Magn Reson Imaging. 2007;25:1130–1137
  4. Szumowski J, Coshow WR, Li F, Quinn SF. Phase unwrapping in the three-point Dixon method for fat suppression MR imaging. Radiology. 1994;192(2):555–561
  5. Rauscher A, Barth M, Herrmann KH, Witoszynskyj S, Deistung A, Reichenbach JR. Improved elimination of phase effects from background field inhomogeneities for susceptibility weighted imaging at high magnetic field strengths. Magn Reson Imaging. 2008;26:1145–1151
  6. Rauscher A, Barth M, Reichenbach JR, Stollberger R, Moser E. Automated unwrapping of MR phase images applied to BOLD MR-venography at 3 Tesla. J Magn Reson Imaging. 2003;18:175–180
  7. Hall DA, Gonçalves MS, Smith S, Jezzard P, Haggard MP, Kornak J. A method for determining venous contribution to BOLD contrast sensory activation. Magn Reson Imaging. 2002;20:695–706
  8. Bakker CJ, de Leeuw H, Vincken KL, Vonken EJ, Hendrikse J. Phase gradient mapping as an aid in the analysis of object-induced and system-related phase perturbations in MRI. Phys Med Biol. 2008;53(18):N349–N358
  9. Bonny JM, Laurent W, Renou JP. Detection of susceptibility effects using simultaneous T2⁎ and magnetic field mapping. Magn Reson Imaging. 2000;18:1125–1128
  10. Hagberg GE, Bianciardi M, Brainovich V, Cassara AM, Maraviglia B. The effect of physiological noise in phase functional magnetic resonance imaging: from blood oxygen level-dependent effects to direct detection of neuronal currents. Magn Reson Imaging. 2008;26:1026–1040
  11. Mills PH, Wu YJL, Ho C, Ahrens ET. Sensitive and automated detection of iron-oxide-labeled cells using phase image cross-correlation analysis. Magn Reson Imaging. 2008;26:618–628
  12. Hedley M, Rosenfeld D. A new two-dimensional phase unwrapping algorithm for MRI images. Magn Reson Med. 1992;24:177–181
  13. Chavez S, Xiang QS, An L. Understanding phase maps in MRI: a new cutline phase unwrapping algorithm. IEEE Trans Med Imaging. 2002;21(8):966–977
  14. Witoszynskyj S, Rauscher A, Reichenbach JR, Barth M. Phase unwrapping of MR images using Phi UN — a fast and robust region growing algorithm. Med Image Anal. 2009;13(2):257–268
  15. Xu W, Cumming I. A region-growing algorithm for InSAR phase unwrapping. IEEE Trans Geosci Remote Sensing. 1999;37(1):124–134
  16. Fornaro G, Sansosti E. A two-dimensional region growing least squares phase unwrapping algorithm for interferometric SAR processing. IEEE Trans Geosci Remote Sensing. 1999;37(5):2215–2226
  17. Jenkinson M. Fast, automated, N-dimensional phase-unwrapping algorithm. Magn Reson Med. 2003;49:193–197
  18. Bioucas-Dias J, Valadão G. Phase unwrapping via graph cuts. IEEE Trans Image Process. 2007;16(3):698–709
  19. Ying L, Liang ZP, David C, Munson J, Koetter R, Frey BJ. Unwrapping of MR phase images using a Markov random field model. IEEE Trans Med Imaging. 2006;25(1):128–136
  20. Ching NH, Rosenfeld D, Braun M. Two-dimensional phase unwrapping using a minimum spanning tree algorithm. IEEE Trans Image Process. 1992;1(3):355–365
  21. An L, Xiang QS, Chavez S. A fast implementation of the minimum spanning tree method for phase unwrapping. IEEE Trans Med Imaging. 2000;19(8):805–808
  22. Song SMH, Napel S, Pelc NJ, Glover GH. Phase unwrapping of MR phase images using Poisson equation. IEEE Trans Image Process. 1995;4(5):667–676
  23. Pritt MD, Shipman JS. Least-squares two-dimensional phase unwrapping using FFT's. IEEE Trans Geosci Remote Sensing. 1994;32(3):706–708
  24. Bagher-Ebadian H, Jiang Q, Ewing JR. A modified Fourier-based phase unwrapping algorithm with an application to MRI venography. J Magn Reson Imaging. 2008;27:649–652
  25. Liang ZP. A model-based method for phase unwrapping. IEEE Trans Med Imaging. 1996;15(6):893–897
  26. Karasev PA, Campbell DP, Richards MA. In: Obtaining a 35× speedup in 2D phase unwrapping using commodity graphics processors. IEEE Radar Conference. Boston, MA: IEEE; 2007;p. 574–578
  27. Ghiglia DC, Romero LA. Minimum LP-norm two-dimensional phase unwrapping. J Opt Soc Am A. 1999;13(10):1999–2013
  28. Teh CH, Chin RT. On image analysis by methods of moments. IEEE Trans Pattern Anal Mach Intell. 1988;10(4):496–513
  29. Hu MK. Visual pattern recognition by moment invariants. IEEE Trans Inf Theory. 1962;8(2):179–187
  30. Smith SM, Jenkinson M, Woolrich MW, Beckmann CF, Behrens TEJ, Johansen-Berg H, et al. Advances in functional and structural MR image analysis and implementation as FSL. NeuroImage. 2004;23(S1):208–219
  31. Fox L, Parker IB. Chebyshev polynomials in numerical analysis. London. New York, [etc.]: Oxford U.P.; 1968;
  32. Zhao Q, Langley J, Faraco C, Miller SL. Correction of susceptibility-induced distortion in diffusion tensor imaging with a moment-based phase unwrapping method. International Journal of Functional Informatics and Personalized Medicine; In press.
  33. Kaplan W. Advanced calculus. Addison-Wesley: Boston; 2002;
  34. Itoh K. Analysis of the phase unwrapping algorithm. Appl Opt. 1982;31(14):2470
  35. Nico G, Fortuny J. Using the matrix pencil method to solve phase unwrapping. IEEE Trans Signal Process. 2003;51(3):886–888
  36. Weisskoff RM. Simple measurement of scanner stability for functional NMR imaging of activation in the brain. Magn Reson Med. 1996;36:643–645
  37. Nico G, Palbinskas G, Datcu M. Bayesian approaches to phase unwrapping: theoretical study. IEEE Trans Signal Process. 2000;48(9):2545–2556

PII: S0730-725X(09)00116-7

doi: 10.1016/j.mri.2009.05.013

Magnetic Resonance Imaging
Volume 27, Issue 9 , Pages 1293-1301 , November 2009

Article Tools

* Image Usage & Resolution