应用复合加权偏微分方程求解的磁共振水脂分离成像算法

Modified Water Fat Separation Algorithm for Magnetic Resonance Imaging with Composite Weight Strategy

提出采用加权多网格方法来求基于相位矩阵的离散偏微分方程的展开解,由最大相位梯度矩阵和相位导数偏差矩阵生成复合标记矩阵,利用标记矩阵标记出相位矩阵中的不连续点和残差点,由此生成加权矩阵来抑制噪声和残差点在偏微分方程求解过程中的误差传播.通过求偏微分方程的加权最小二乘解,引导相位展开从相位质量高的点开始,有效避开低质量区域,不仅提高了相位展开的可靠性,而且能够正确地实现噪声条件下的相位展开.通过仿真数据和临床常见的头部磁共振成像,以及在0.3T低场永磁型磁共振系统上的实验结果,证明了该算法的有效性.

Phase unwrapping methods are discussed for water fat separation in magnetic resonance imaging （MRI）. Weighted multi-grid algorithm is applied to solve the discrete partial differential equation of phase array. A new weight method is propased, which is composed from maximum gradient array and phase differential coefficient array. The residues and discontinuous points are labeled by this composed weight array, where the error propagation the process of can be restrained by residues and noises during solving the discrete partial differential equation. By means of the weighted least squares solutions for partial differential equations, the phase unwrapping starts from the high-quality regions and avoids the low-quality regions effectively to improve the reliability. The simulation data and experiments for brain scan on 0.3 T low field MRI system show the validity.