Quantitation using the magnitude of the reconstructed magnetic resonance (MR) image is the predominant practice in various clinical applications. Recently, the phase of the MR signal has demonstrated its promise in expanding the quantitative capability of magnetic resonance imaging (MRI). For example, the phase signal has been directly linked with Electro-Magnetic (EM) properties of tissues (such as susceptibility and conductivity), tissue temperature, venous oxygenation, blood velocity, and tissue elasticity, among others, as described in References [1-6] listed herein before the Claims section. The MR phase has also been extensively used for “fieldmap estimation” in the neuroimaging community to calculate and correct for the inhomogeneity of the static field, as described in Refs. [7-11]. Reference [7], “Highresolution, large dynamic range field map estimation,” Magnetic Resonance in Medicine. 2014 January; 71(1):105-17, by Dagher and Bilgin is incorporated herein by reference in its entirety.
Combining MR phase images from multiple receiver coils is a challenging problem, complicated by MR phase measurement errors that hinder accurate determination of MR signal phase. These MR phase measurement errors are introduced by phase wrapping, noise and the unknown phase-offset between the receiver coils of the MRI scanner. Various techniques have been proposed to mitigate the effect of these MR phase measurement errors but most of the existing methods require additional reference scans and/or use ad-hoc post-processing techniques that do not guarantee optimality.