Schiecke K, Schmidt C, Piper D, Putsche P, Feucht M, Witte H, Leistritz L
Karin Schiecke, Institute of Medical Statistics, Computer Sciences and Documentation, Jena University Hospital, Friedrich Schiller University Jena, Bachstr. 18, 07740 Jena, Germany, E-mail:
Methods Inf Med. 2015;54(5):461-73. doi: 10.3414/ME14-02-0024. Epub 2015 Sep 30.
Empirical mode decomposition (EMD) is a frequently used signal processing approach which adaptively decomposes a signal into a set of narrow-band components known as intrinsic mode functions (IMFs). For multi-trial, multivariate (multiple simultaneous recordings), and multi-subject analyses the number and signal properties of the IMFs can deviate from each other between trials, channels and subjects. A further processing of IMFs, e.g. a simple ensemble averaging, should determine which IMFs of one signal correspond to IMFs from another signal. When the signal properties have similar characteristics, the IMFs are assigned to each other. This problem is known as correspondence problem.
From the mathematical point of view, in some cases the correspondence problem can be transformed into an assignment problem which can be solved e.g. by the Kuhn-Munkres algorithm (KMA) by which a minimal cost matching can be found. We use the KMA for solving classic assignment problems, i.e. the pairwise correspondence between two sets of IMFs of equal cardinalities, and for pairwise correspondences between two sets of IMFs with different cardinalities representing an unbalanced assignment problem which is a special case of the k-cardinality assignment problem.
A KMA-based approach to solve the correspondence problem was tested by using simulated, heart rate variability (HRV), and EEG data. The KMA-based results of HRV decomposition are compared with those obtained from a hierarchical cluster analysis (state-of-the-art). The major difference between the two approaches is that there is a more consistent assignment pattern using KMA. Integrating KMA into complex analysis concepts enables a comprehensive exploitation of the key advantages of the EMD. This can be demonstrated by non-linear analysis of HRV-related IMFs and by an EMD-based cross-frequency coupling analysis of the EEG data.
The successful application to HRV and EEG analysis demonstrates that our solutions can be used for automated EMD-based processing concepts for biomedical signals.
经验模态分解（EMD）是一种常用的信号处理方法，它能将一个信号自适应地分解为一组称为本征模态函数（IMF）的窄带分量。对于多试验、多变量（多个同步记录）和多受试者分析，IMF的数量和信号特性在不同试验、通道和受试者之间可能会相互偏离。对IMF进行进一步处理，例如简单的总体平均，应该确定一个信号的哪些IMF与另一个信号的IMF相对应。当信号特性具有相似特征时，将IMF相互分配。这个问题被称为对应问题。
从数学角度来看，在某些情况下，对应问题可以转化为一个分配问题，例如可以通过库恩 - 蒙克雷斯算法（KMA）来解决，通过该算法可以找到最小成本匹配。我们使用KMA来解决经典的分配问题，即两组等基数IMF之间的成对对应，以及两组基数不同的IMF之间的成对对应，这代表了一个不平衡分配问题，它是k基数分配问题的一个特殊情况。
通过使用模拟数据、心率变异性（HRV）数据和脑电图（EEG）数据，测试了一种基于KMA解决对应问题的方法。将基于KMA的HRV分解结果与通过层次聚类分析（当前技术水平）获得的结果进行比较。这两种方法的主要区别在于，使用KMA时有更一致的分配模式。将KMA集成到复杂的分析概念中能够全面利用EMD的关键优势。这可以通过对与HRV相关的IMF进行非线性分析以及对EEG数据进行基于EMD的交叉频率耦合分析来证明。
成功应用于HRV和EEG分析表明，我们的解决方案可用于基于EMD的生物医学信号自动化处理概念。
