Two-dimensional phase unwrapping using a minimum spanning tree algorithm
Two-dimensional phase unwrapping using a minimum spanning tree algorithm
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DOI：
10.1109/83.148608
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发表时间：
1992-07-01
影响因子：
10.6
通讯作者：
Braun, Michael
中科院分区：
文献类型：
--
作者：
Ching, Neng H.;Rosenfeld, Dov;Braun, Michael
相位展开是指从模2 pi数据中确定相位。一些相位数据可能不可靠（例如，当幅度接近于零或信噪比较差时）。在二维中，这相当于将相函数的支持限制在一个或多个任意形状的区域。提出了一种相位展开算法，该算法适用于仅在一组可能具有非凸边界的非连通区域内已知的二维数据。该算法包括以下步骤：分段识别连通性，使用泰勒级数展开每个段内的相位展开，沿着最优路径在未连接的段之间进行相位展开，以及填充相位信息空白。采用最小生成树算法确定段间展开的最优路径。虽然该算法适用于任何二维数据，但其主要应用是磁共振成像（MRI），其中相图可用于确定外加磁场的分布、物体固有的化学位移和物体的磁化率。
Phase unwrapping refers to the determination of phase from modulo 2 pi data. Some of the phase data may not be reliable (e.g., where the magnitude approaches zero or where the signal-to-noise ratio is poor). In two dimensions, this is equivalent to confining the support of the phase function to one or more arbitrarily shaped regions. A phase unwrapping algorithm is presented which works for two-dimensional (2-D) data known only within a set of nonconnected regions with possibly nonconvex boundaries. The algorithm includes the following steps: segmentation to identify connectivity, phase unwrapping within each segment using a Taylor series expansion, phase unwrapping between disconnected segments along an optimum path, and filling of phase information voids. The optimum path for intersegment unwrapping is determined by a minimum spanning tree algorithm. Although the algorithm is applicable to any 2-D data, the main application addressed is magnetic resonance imaging (MRI) where phase maps are useful in determining the distributions of the applied magnetic field, inherent chemical shifts of the object, and the object's magnetic susceptibility.