title: A modified Fourier-based phase unwrapping algorithm with an application to MRI venography.
abstract: OBJECTIVE
  To present a single-step deterministic procedure for unwrapping MRI phase maps.
  
  
  METHODS
  Using an algorithm previously developed for optical applications, Laplacian operators were applied in the Fourier space of the MRI phase map. The original Fourier-based phase unwrapping algorithm was modified so that demodulation accomplished the required signal symmetrization in Fourier space. To evaluate the method's performance in the presence of thermal noise, a set of wrapped phase maps were simulated at different levels of noise in k-space, and the response of the algorithm at different levels of signal-to-noise ratio (SNR) was evaluated for stability. To demonstrate its utility in MRI, the algorithm was applied to the wrapped phase maps of susceptibility-weighted imaging (SWI) studies, which were then used to generate venograms.
  
  
  RESULTS
  In simulated phase wrapping, the algorithm correctly reproduced the original phase for a wide range of phase gradients and noise. The procedure was fast and produced useful maps of venous structures in SWI images.
  
  
  CONCLUSIONS
  A fast and stable single-step deterministic method for unwrapping MRI phase maps is available for such applications as SWI and mapping of static magnetic field inhomogeneity.
authors.affiliation: Department of Neurology, Henry Ford Hospital, Detroit, MI 48202, USA.
authors.forename: Hassan
authors.initials: H
authors.lastname: Bagher-Ebadian
authors.forename: Quan
authors.initials: Q
authors.lastname: Jiang
authors.forename: James R
authors.initials: JR
authors.lastname: Ewing
mesh_terms: D000465:Algorithms; D006801:Humans; D008279:Magnetic Resonance Imaging / Q000379:methods*; D010690:Phlebography; D014680:Veins / Q000033:anatomy & histology*