Objective

2

An accurate phase map is crucial for magnetic resonance imaging (MRI)-based clinical applications

such as two-point and three-point Dixon techniques

susceptibility-weighted imaging

and human-brain phase imaging. However

the phase calculated from the complex MR signal is commonly wrapped back into the range of (-π

π] for the arctangent operation. Phase unwrapping is required to recover the underlying actual phase. A certain number of phase unwrapping methods have been proposed under the assumption that the underlying actual phase difference between adjacent pixels should not be larger than π. If the wrapped phase map contains severe noise

rapid phase change

or even disconnected regions in the interesting region

then the underlying actual phase difference between adjacent pixels may be larger than π; thus

this assumption becomes invalid. A new phase-unwrapping method is proposed; this method is based on phase partition and local polynomial surface fitting

which works robustly under the situation of severe noise

rapid phase changes

and disconnected regions.

Method

2

The proposed method first exploits the phase partition method to split the acquired phase map into the connected blocks. The phase inside each block remains within a given interval

and the wrapped phase difference between adjacent pixels is less than π. Therefore

no phase wrap exists inside each block. To reduce the affection of noise

the blocks with pixel number of less than a given threshold (such as 50) are clustered into residual pixels. Then

the proposed method sequentially performs inter-block phase unwrapping and residual-pixel phase unwrapping by a region-growing local polynomial surface fitting approach. Three simulated datasets were separately generated with signal-to-noise ratios (SNRs) varying from 6.5 to 0.5

phase height changing from 100 rad to 200 rad

and disconnected regions to test the performance of the proposed method on the data under the situation of severe noise

different phase change levels and disconnected regions. The three-point Dixon knee and ankle data of five healthy adult human volunteers were acquired on a 0.35 T permanent magnet MR scanner to test the performance of the proposed method on the in vivo MR data (XGY-OPER

Ningbo Xingaoyi

Ningbo

China). In addition

the two-point Dixon knee data of one healthy volunteer were acquired on a 3.0 T MR scanner (Philips

Achieva

Netherlands). The simulation and in vivo two-point and three-point water-fat Dixon data were used to evaluate the proposed method and compared with phase-region expanding labeler for unwrapping discrete estimates (PRELUDE). The unwrapped error ratio was calculated as the number of inaccurate unwrapped pixels divided by the total number of pixels to quantitatively evaluate the performance of the proposed method. Each simulation was repeated 20 times

and the corresponding means and standard deviations (SDs) of unwrapped error ratio (%) were calculated. The unwrapped results were implemented via Dixon technique to produce water and fat images to evaluate the performance of the proposed method on in vivo data. If the phase-unwrapping method does not acquire an accurate phase map

then the water and fat images will contain swaps. The water-fat separation results of every slice were evaluated by a blinded board-certified radiologist according to the following four-point scale: 1) many swaps (slices)

2) few swaps (slices)

3) total swap slices

and 4) error ratio.

Result

2

1) In the simulation experiment of different signal-to-noise ratio (SNR) levels

the phase map unwrapped by PRELUDE contains evident wrapping residues in low SNR regions. However

the unwrapped error is substantively reduced in the results generated by the proposed method. The proposed method consistently produced a substantially lower mean and SD of unwrapped error ratio than those of PRELUDE when SNR is below 2.5. 2) In the simulation experiment of different phase change levels

the unwrapped results produced by PRELUDE contain evident wraps when the phase height increased to 200 rad. On the contrary

the proposed method consistently produced accurate unwrapped results for different phase heights. 3) In the simulation experiment of existing discontented regions

PRELUDE generated results with serious wrapping residues

and the mean and SD of the unwrapped error ratio was 12.79±0.67 (%). The proposed method produced an accurate unwrapped phase with the mean and SD of unwrapped error ratio of 0.10±0.05 (%). 4) In the in vivo 0.35 T datasets of five volunteers and the 3.0 T dataset of one volunteer (a total of 100 slices

consisting of 75 sagittal knees and 25 sagittal ankles) water-fat separation experiments

the results generated by PRELUDE had nine times many swaps and 33 times few swaps out of 100 outputs. Meanwhile

the proposed method only produced six times few swaps. The total error ratio of PRELUDE was 42% and that of the proposed method was only 6%.

Conclusion

2

A new phase-unwrapping method

which first splits the acquired phase map into connected blocks by exploiting the phase partition method

is presented. The blocks with the pixel number of less than a given threshold are clustered into the residual pixels. Then

the proposed method sequentially performs inter-block phase unwrapping and residual-pixel phase unwrapping by using a region-growing local polynomial surface fitting approach. The simulation results demonstrate that the proposed method can achieve robust and accurate phase unwrapping even under serious noise

rapid phase changes

and disconnected regions. The application on two-point and three-point water-fat Dixon MRI data shows that the proposed method can successfully separate water and fat with few swaps. Therefore

the proposed method is beneficial to phase-related MRI applications

such as two-point and three-point Dixon techniques

susceptibility-weighted imaging

and human-brain phase imaging.