磁共振成像二维相位解缠方法研究
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摘要
磁共振成像得到的信号是复数形式,包含幅度和相位。常规诊断中,往往用到的是磁共振的幅度图像。然而,其相位也包含了大量信息,例如自旋原子核的移动速度、磁场的不均匀度和磁化率变化等。因此磁共振相位可以用来估计主磁场均匀性和获取临床相关的生理参数。
但从复数信号中提取真实相位时,相位值却会被限制在(-π,π)弧度区间内,位于该区间外的真实相位被缠绕到这一区间内。此现象称为相位缠绕,得到的相位称为缠绕相位。从缠绕相位恢复真实相位的过程就叫做相位解缠。噪声、欠采样和物体不连续的存在使相位解缠变得困难。
本文提出了三种新的二维相位解缠方法。模拟数据和实际磁共振相位数据被用来评估这些方法的表现。
第一种方法是基于离散粒子群优化算法的枝切线法。这种方法先将整幅图像的残差分成几组；在每组内使用离散粒子群优化算法对正负极性残差进行配对；用枝切线连接每组内配好对的正负极性残差；最后绕过这些枝切线进行相位解缠。
与最新的基于人工智能的枝切法对比,这种方法能在较短时间内得到合理的枝切线连接,且通过对残差分组进一步降低了计算时间。
第二种相位解缠方法是基于直接求解法的加权最小Lp范数法。它将整个相位图像的解缠相位梯度与缠绕相位梯度之间差值的加权Lp范数作为优化目标函数；将这个目标函数转化成一个方程组,其系数矩阵采用稀疏结构储存和表达；最后使用直接求解法求解方程组。由于方程组的系数矩阵与解缠相位有关,因此采取迭代方式得到最终的解缠结果。
与一些常用方法相比,这种方法能有效减少计算时间且解缠结果更准确。
第三种方法是基于掩码的区域增长法。这种方法采用一种新的掩码提取方式将残差合理地连接起来作为掩码中的零点；将掩码与相位导数方差结合构成最终的质量图,这样连接残差经过的点均被当成零质量(也就是质量最差)的点,会被滞留到最后才被相位解缠；接着根据质量图将整幅图像分成多个区域,在每个区域内单独进行相位解缠,其中质量最差的那个区域从多个方向进行相位加权平均；最后将多个区域融合在一起。
与最新的区域增长相位解缠方法(PHUN)相比,这种方法运算速度快并能够限制误差的传播。
In magnetic resonance imaging (MRI), the complex signal contains both the magnitude and phase parts. Usually the magnitude of the MRI signal has been mainly considered. However, the phase of MRI signal offers very important information on the velocity of the moving spins, the main Bo field inhomogeneity, the magnetic susceptibility variations, etc. So the phase can be used to estimate the main B0field inhomogeneity and obtain clinically relevant physiological parameters.
when extracting the phase from a measured complex MR dataset through some mathematical operation, the result is typically wrapped into the principal interval of (-π,π] radians, producing the wrapped phase. The process of estimating the true phase from the wrapped phase is called phase unwrapping. Because of the presence of the noise, undersampling and/or object discontinuities, phase unwrapping becomes intractable and nontrivial. In the literature, there are quite a few existing phase unwrapping algorithms.
In this thesis, three two-dimensional (2D) phase unwrapping methods were proposed. Both simulated and MR data were used to evaluate these algorithms' performances.
(1) A new branch-cut method based on discrete particle swarm optimization (dPSO) algorithm was proposed to solve the phase unwrapping problem of MR data. In this method, all the residues were first grouped by dividing the phase image into sub-regions. Then dPSO was performed region by region to match the opposite polarity residues which were connected by branch cuts afterward. Finally, flood-fill method was used to unwrap phases avoiding these branch cuts. Compared with conventionally used branch-cut phase unwrapping algorithms, the dPSO algorithm is rather robust and effective.
(2) A direct-solver-based weighted minimum Lp-norm algorithm was proposed for MRI phase unwrapping. First, the algorithm converted the weighted minimum-Lp-norm objective function for phase unwrapping into a linear system of equations whose system (coefficient) matrix was a large, symmetric one. Then, the coefficient-matrix was represented in the sparse structure. Finally, standard direct solvers were employed to solve this linear system. The results demonstrate that the proposed algorithm is reliable and robust.
(3) A mask-based region growing approach was proposed for MRI phase unwrapping. The residues were first connected by zero-value pixels that were then served as mask. And the mask and the original quality map were combined into a new quality map. Guided by the new quality map, unwrapping was carried out within multiple regions. At last, the regions were merged by adjusting the offset between one another. The results show the advantage of the proposed approach over the recent region-growing phase unwrapping method (PHUN) in accuracy.
但从复数信号中提取真实相位时,相位值却会被限制在(-π,π)弧度区间内,位于该区间外的真实相位被缠绕到这一区间内。此现象称为相位缠绕,得到的相位称为缠绕相位。从缠绕相位恢复真实相位的过程就叫做相位解缠。噪声、欠采样和物体不连续的存在使相位解缠变得困难。
本文提出了三种新的二维相位解缠方法。模拟数据和实际磁共振相位数据被用来评估这些方法的表现。
第一种方法是基于离散粒子群优化算法的枝切线法。这种方法先将整幅图像的残差分成几组；在每组内使用离散粒子群优化算法对正负极性残差进行配对；用枝切线连接每组内配好对的正负极性残差；最后绕过这些枝切线进行相位解缠。
与最新的基于人工智能的枝切法对比,这种方法能在较短时间内得到合理的枝切线连接,且通过对残差分组进一步降低了计算时间。
第二种相位解缠方法是基于直接求解法的加权最小Lp范数法。它将整个相位图像的解缠相位梯度与缠绕相位梯度之间差值的加权Lp范数作为优化目标函数；将这个目标函数转化成一个方程组,其系数矩阵采用稀疏结构储存和表达；最后使用直接求解法求解方程组。由于方程组的系数矩阵与解缠相位有关,因此采取迭代方式得到最终的解缠结果。
与一些常用方法相比,这种方法能有效减少计算时间且解缠结果更准确。
第三种方法是基于掩码的区域增长法。这种方法采用一种新的掩码提取方式将残差合理地连接起来作为掩码中的零点；将掩码与相位导数方差结合构成最终的质量图,这样连接残差经过的点均被当成零质量(也就是质量最差)的点,会被滞留到最后才被相位解缠；接着根据质量图将整幅图像分成多个区域,在每个区域内单独进行相位解缠,其中质量最差的那个区域从多个方向进行相位加权平均；最后将多个区域融合在一起。
与最新的区域增长相位解缠方法(PHUN)相比,这种方法运算速度快并能够限制误差的传播。
In magnetic resonance imaging (MRI), the complex signal contains both the magnitude and phase parts. Usually the magnitude of the MRI signal has been mainly considered. However, the phase of MRI signal offers very important information on the velocity of the moving spins, the main Bo field inhomogeneity, the magnetic susceptibility variations, etc. So the phase can be used to estimate the main B0field inhomogeneity and obtain clinically relevant physiological parameters.
when extracting the phase from a measured complex MR dataset through some mathematical operation, the result is typically wrapped into the principal interval of (-π,π] radians, producing the wrapped phase. The process of estimating the true phase from the wrapped phase is called phase unwrapping. Because of the presence of the noise, undersampling and/or object discontinuities, phase unwrapping becomes intractable and nontrivial. In the literature, there are quite a few existing phase unwrapping algorithms.
In this thesis, three two-dimensional (2D) phase unwrapping methods were proposed. Both simulated and MR data were used to evaluate these algorithms' performances.
(1) A new branch-cut method based on discrete particle swarm optimization (dPSO) algorithm was proposed to solve the phase unwrapping problem of MR data. In this method, all the residues were first grouped by dividing the phase image into sub-regions. Then dPSO was performed region by region to match the opposite polarity residues which were connected by branch cuts afterward. Finally, flood-fill method was used to unwrap phases avoiding these branch cuts. Compared with conventionally used branch-cut phase unwrapping algorithms, the dPSO algorithm is rather robust and effective.
(2) A direct-solver-based weighted minimum Lp-norm algorithm was proposed for MRI phase unwrapping. First, the algorithm converted the weighted minimum-Lp-norm objective function for phase unwrapping into a linear system of equations whose system (coefficient) matrix was a large, symmetric one. Then, the coefficient-matrix was represented in the sparse structure. Finally, standard direct solvers were employed to solve this linear system. The results demonstrate that the proposed algorithm is reliable and robust.
(3) A mask-based region growing approach was proposed for MRI phase unwrapping. The residues were first connected by zero-value pixels that were then served as mask. And the mask and the original quality map were combined into a new quality map. Guided by the new quality map, unwrapping was carried out within multiple regions. At last, the regions were merged by adjusting the offset between one another. The results show the advantage of the proposed approach over the recent region-growing phase unwrapping method (PHUN) in accuracy.
引文
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