New 3D phase-unwrapping method based on voxel clustering and local polynomial modeling: application to quantitative susceptibility mapping

Background: To develop an accurate and robust 3-dimensional (3D) phase-unwrapping method that works effectively in the presence of severe noise, disconnected regions, rapid phase changes, and open-ended lines for quantitative susceptibility mapping (QSM).

Methods: We developed a 3D phase-unwrapping method based on voxel clustering and local polynomial modeling named CLOSE3D, which firstly explores the 26-neighborhood to calculate local variation of the phasor and the phase, and then according to the local variation of the phasor, clusters the phase data into easy-to-unwrap blocks and difficult-to-unwrap residual voxels. Next, CLOSE3D sequentially performs intrablock, interblock, and residual-voxel unwrapping by using the region-growing local polynomial modeling method. CLOSED3D was evaluated in simulation and using in vivo brain QSM data, and was compared with classical region-growing and region-expanding labeling for unwrapping estimates methods.

Results: The simulation experiments showed that CLOSE3D achieved accurate phase-unwrapping results with a mean error ratio <0.39%, even in the presence of serious noise, disconnected regions, and rapid phase changes. The error ratios of region-growing (P=0.000 and P=0.000) and region-expanding labeling for unwrapping estimates (P=0.007, P=0.014) methods were both significantly higher than that of CLOSE3D, when the noise level was ≥60%. The results of the in vivo brain QSM experiments showed that CLOSE3D unwrapped the phase data and accurately reconstructed quantitative susceptibility data, even with serious noise, rapid-varying phase, or an open-ended cutline.

Conclusions: CLOSE3D achieves phase unwrapping with high accuracy and robustness, which will help phase-related 3D magnetic resonance imaging (MRI) applications such as QSM and susceptibility weighted imaging.