Correction of phase wrapping in magnetic resonance imaging

Abstract

In phase reconstruction MR imaging, e.g., for velocity measurement, phase shifts beyond +/- pi radians will "wrap around" to smaller apparent phases. Such large phase shifts could arise either due to large background (non-flow-related) phase variations or due to large velocity-induced phase shifts. For sufficiently smooth phase variation, such discontinuities can be automatically recognized and corrected, thus restoring the correct phase values and extending the effective dynamic range of such phase imaging techniques.

NMR probes for measuring magnetic fields and field dynamics in MR systems

“…The latter is necessary to reconstruct continuous phase time courses from the measured phase values, which are determined only modulo 2 (36). If the probe signal were sampled near the Nyquist sampling limit for the NMR signal content there is a risk of unwrapping errors due to phase noise.…”

Absolute phase image reconstruction: a stochastic nonlinear filtering approach

“…References [20], [25], [29], [36], [42], [43], [45], [52], and [55] describe applications to InSAR. Phase unwrapping techniques for MRI have been presented in [4], [12], [30], and [54]. In the field of optical interferometry, several methods were published in [28], [46], [47], [51], and [57].…”

“…• Magnetic resonance imaging (MRI), in which absolute phase measurements allow increasing the dynamic range of phase contrast velocity images; references [4], [12], [30], and [54] consider this problem.…”

Spatiotemporal magnetic field monitoring for MR

“…The phase φ j (t) of demodulated probe signals is determined only modulo 2π , requiring so-called phase unwrapping to reconstruct continuous phase time courses (32). Unwrapping of one-dimensional signals is straightforward and robust provided sufficient signal-to-noise ratio (SNR) and sampling rate.…”