• Lei Ying, Zhi-Pei Liang, David C Munson, Ralf Koetter, and Brendan J Frey.
• Department of Electrical Engineering and Computer Science, University of Wisconsin, Milwaukee, WI 53201, USA. leiying@uwm.edu
• IEEE Trans Med Imaging. 2006 Jan 1; 25 (1): 128-36.

AbstractPhase 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.

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