title: Nonlinear phase correction with an extended statistical algorithm.
abstract: This paper presents a new magnetic resonance imaging (MRI) phase correction method. The linear phase correction method using autocorrelation proposed by Ahn and Cho (AC method) is extended to handle nonlinear terms, which are often important for polynomial expansion of phase variation in MRI. The polynomial coefficients are statistically determined from a cascade series of n-pixel-shift rotational differential fields (RDFs). The n-pixel-shift RDF represents local vector rotations of a complex field relative to itself after being shifted by n pixels. We have found that increasing the shift enhances the signal significantly and extends the AC method to handle higher order nonlinear phase error terms. The n-pixel-shift RDF can also be applied to improve other methods such as the weighted least squares phase unwrapping method proposed by Liang. The feasibility of the method has been demonstrated with two-dimensional (2-D) in vivo inversion-recovery MRI data.
authors.affiliation: Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1ZI, Canada. chang@physics.ubc.ca
authors.forename: Zheng
authors.initials: Z
authors.lastname: Chang
authors.forename: Qing-San
authors.initials: QS
authors.lastname: Xiang
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D003198:Computer Simulation; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted