Extending the dynamic range of phase contrast magnetic resonance velocity imaging using advanced higher-dimensional phase unwrapping algorithms.

Phase contrast magnetic resonance velocity imaging is a powerful technique for quantitative in vivo blood flow measurement. Current practice normally involves restricting the sensitivity of the technique so as to avoid the problem of the measured phase being 'wrapped' onto the range -pi to +pi. However, as a result, dynamic range and signal-to-noise ratio are sacrificed. Alternatively, the true phase values can be estimated by a phase unwrapping process which consists of adding integral multiples of 2pi to the measured wrapped phase values. In the presence of noise and data undersampling, the phase unwrapping problem becomes non-trivial. In this paper, we investigate the performance of three different phase unwrapping algorithms when applied to three-dimensional (two spatial axes and one time axis) phase contrast datasets. A simple one-dimensional temporal unwrapping algorithm, a more complex and robust three-dimensional unwrapping algorithm and a novel velocity encoding unwrapping algorithm which involves unwrapping along a fourth dimension (the 'velocity encoding' direction) are discussed, and results from the three are presented and compared. It is shown that compared to the traditional approach, both dynamic range and signal-to-noise ratio can be increased by a factor of up to five times, which demonstrates considerable promise for a possible eventual clinical implementation. The results are also of direct relevance to users of any other technique delivering time-varying two-dimensional phase images, such as dynamic speckle interferometry and synthetic aperture radar.

Robust fringe density and direction estimation in noisy phase maps.

A method for automated fringe analysis is presented. It robustly estimates local fringe density and direction in noisy wrapped phase maps. Such information can be used to improve the performance of two-dimensional phase unwrapping methods, to construct phase-jump-preserving filtering strategies, and also to perform robust segmentation of phase data. The method, which is highly insensitive to noise, is model based and performs the estimation in the Fourier domain.

An anisotropic evolution formulation applied in 2-D unwrapping of discontinuous phase surfaces.

In this paper, a new method to reconstruct piecewise continuous phase estimates using inphase and quadrature components acquired from interferometry measurements is derived and discussed. The method, based on the concept of anisotropic evolution formulations, is shown to be far less noise sensitive than similar methods operating on modulo-mapped data (i.e., traditional phase unwrapping methods). The method is able to produce reliable phase estimates from data containing complex sheared structures in combination with high noise content without relying on user-defined weights.