发布时间: 2018-06-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.170515 2018 | Volume 23 | Number 6 医学图像处理

1. 电子科技大学自动化工程学院, 成都 611731;
2. 南方医科大学生物医学工程学院, 广州 510515
 收稿日期: 2017-09-22; 修回日期: 2018-01-03 基金项目: 国家自然科学基金项目（61471188） 第一作者简介: 程军营(1988-), 男, 电子科技大学控制科学与工程专业博士研究生, 主要研究方向为磁共振相位成像。E-mail:xuanyu880224@126.com. 中图法分类号: TP391 文献标识码: A 文章编号: 1006-8961(2018)06-0906-11

# 关键词

New phase-unwrapping method based on phase partition and local polynomial surface fitting
Cheng Junying1,2, Wang Changqing1,2, Feng Yanqiu1, Chen Wufan1,2
1. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;
2. School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China
Supported by: National Natural Science Foundation of China (61471188)

# Abstract

Objective 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 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 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 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.

# Key words

magnetic resonance imaging; phase unwrapping; phase partition; local polynomial surface fitting; water-fat separation

# 1.1 相位解缠绕问题

 $\varphi = \angle S$ (1)

 $\phi = \varphi + 2k\pi$ (2)

$k$ 是整数。相位解缠绕就是为相位图中的每一个像素都找到一个正确的相位补偿 $k$ 来恢复真实相位。

# 1.2 局部多项式曲面拟合

 ${\phi _{(x,y)}} = \sum\limits_{m = 0}^M {\sum\limits_{n = 0}^N {{C_{m,n}}{x^m}{y^n} + {e_{(x,y)}}} }$ (3)

 $\mathit{\pmb{\Phi }} = \mathit{\boldsymbol{X\hat c}} + \mathit{\boldsymbol{E}}$ (4)

 ${\phi _{({x_0},{y_0})}} = R\left( {\frac{{{X_{({x_0},{y_0})}}\hat c - {\varphi _{({x_0},{y_0})}}}}{{2\pi }}} \right) \times 2\pi + {\varphi _{({x_0},{y_0})}}$ (5)

# 1.3 提出方法

1) 选取最靠近已解缠绕区域的残余像素；

2) 对步骤1)获得残余像素，根据其幅值大小按降序排列；

3) 根据步骤2)确定的先后顺序，根据式(4)(5)，使用以生长点为中心的局部窗内已解缠绕像素的相位来对生长点相位解缠绕；

4) 重复步骤1)2)3)直至所有的残余像素完成解缠绕。

# 3.1 仿真实验

Table 1 Means and standard deviations of errors ration using the two methods over 20 repetitions under different SNRs

 /% 节 信噪比 PRELUDE 提出方法 1 6 0.00±0.00 0.00±0.00 2 5.5 0.00±0.00 0.00±0.00 3 5 0.00±0.00 0.00±0.00 4 4.5 0.00±0.00 0.00±0.00 5 4 0.00±0.00 0.00±0.00 6 3.5 0.00±0.00 0.00±0.00 7 3 0.00±0.00 0.00±0.00 8 2.5 0.01±0.01 0.00±0.00 9 2 0.06±0.03 0.01±0.01 10 1.5 0.35±0.12 0.09±0.04 11 1 1.81±0.30 0.19±0.10 12 0.5 6.43±1.32 0.51±0.24

# 3.2 真实磁共振成像实验

Table 2 Statistical results of slices with swaps in the water-fat separation datasets of 6 volunteers

 数据集 方法 很多互换 较少互换 错误层数 错误率/% 膝关节(0.35 T) PRELUDE 2 7 9 18.00 本文 0 2 2 4.00 踝关节(0.35 T) PRELUDE 1 11 12 48.00 本文 0 3 3 12.00 膝关节(3.0 T) PRELUDE 6 15 21 84.00 本文 0 1 1 4.00 总数 PRELUDE 9 33 42 42.00 本文 0 6 6 6.00

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