Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping.

Applied Optics
M F SalfityD A Beauregard

Abstract

We demonstrate in both simulated and real cases the effect that undersampling of a three-dimensional (3D) wrapped phase distribution has on the geometry of phase singularity loops and their branch cut surfaces. The more intuitive two-dimensional (2D) problem of setting branch cuts between dipole pairs is taken as a starting point, and then branch cut surfaces in flat and ambiguous 3D loops are discussed. It is shown that the correct 2D branch cuts and 3D branch cut surfaces should be placed where the gradient of the original phase distribution exceeded pi rad voxel(-1). This information, however, is lost owing to undersampling and cannot be recovered from the sampled wrapped phase distribution alone. As a consequence, empirical rules such as finding the surface of minimal area or methods based on the wrapped phase gradient will fail to find the correct branch cut surfaces. We conclude that additional information about the problem under study is therefore needed to produce correct branch cut surfaces that lead to an unwrapped phase distribution with minimum local errors. An example with real data is provided in which downsampled phase contrast magnetic resonance imaging data are successfully unwrapped when the position of the ve...Continue Reading

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Citations

Jan 11, 2012·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Junmin Liu, Maria Drangova
Jan 26, 2010·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Kevin M Johnson, Michael Markl
May 25, 2011·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Yongchang WangLaurence G Hassebrook
Jul 9, 2016·Korean Journal of Radiology : Official Journal of the Korean Radiological Society·Hojin HaNamkug Kim
Aug 13, 2009·Physics in Medicine and Biology·Jason Langley, Qun Zhao
Nov 12, 2009·Applied Optics·Miguel Arevalillo-HerráezDavid R Burton
Aug 12, 2009·Applied Optics·Hussein Abdul-RahmanMohammed Qudeisat
Dec 4, 2012·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Semanti Chakraborty, Pablo D Ruiz
Jun 3, 2010·Applied Optics·Jason A LangleyQun Zhao

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