Unwrapping of MR phase images using a Markov random field model

Lei Ying, Zhi Pei Liang, D. C. Munson, R. Koetter, B. J. Frey

Research output: Contribution to journalArticlepeer-review


Phase unwrapping is an important problem in many magnetic resonance imaging applications, such as field mapping and flow imaging. The challenge in two-dimensional phase unwrapping lies in distinguishing jumps due to phase wrapping from those due to noise and/or abrupt variations in the actual function. This paper addresses this problem using a Markov random field to model the true phase function, whose parameters are determined by maximizing the a posteriori probability. To reduce the computational complexity of the optimization procedure, an efficient algorithm is also proposed for parameter estimation using a series of dynamic programming connected by the iterated conditional modes. The proposed method has been tested with both simulated and experimental data, yielding better results than some of the state-of-the-art method (e.g., the popular least-squares method) in handling noisy phase images with rapid phase variations.

Original languageEnglish (US)
Pages (from-to)128-136
Number of pages9
JournalIEEE transactions on medical imaging
Issue number1
StatePublished - Jan 2006
Externally publishedYes


  • A posteriori probability
  • Aphilipp
  • Computational complexity
  • Field mapping
  • Flow imaging
  • Least-squares method
  • Magnetic resonance imaging
  • Markov random field model
  • MR phase images
  • Optimization
  • Parameter estimation
  • Phase unwrapping

ASJC Scopus subject areas

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Computational Theory and Mathematics


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