Joint Empirical Mode Decomposition and Sparse Binary Programming for Underlying Trend Extraction
Joint Empirical Mode Decomposition and Sparse Binary Programming for Underlying Trend Extraction
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用于底层趋势提取的联合经验模式分解和稀疏二值规划
DOI：
10.1109/tim.2013.2265451
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发表时间：
2013-06
影响因子：
5.6
通讯作者：
Bingham, C.
中科院分区：
文献类型：
--
作者：
Zhijing Yang;Ling, B.W.-K.;Bingham, C.
本文提出了一种新的方法，通过联合经验模式分解（EMD）和稀疏二进制规划方法提取信号的潜在趋势。将EMD应用于信号，并获得相应的本征模式函数（IMF）。信号的潜在趋势通过IMF的和来获得，其中这些IMF被选择或丢弃。所选择的IMF的总数被最小化，服从关于去噪信号（通过丢弃第一IMF而获得的信号）与潜在趋势之间的最大绝对差的规范。由于所选择的IMF的总数被最小化，因此所获得的解是稀疏的，并且仅选择少数IMF。所选择的IMF对应于信号的潜在趋势的分量。另一方面，L ∞范数规范保证了潜在趋势和去噪信号之间的最大绝对差由可接受的水平限制。这迫使潜在趋势跟随全球信号的变化。当IMF被选择或丢弃时，系数为零或一。该问题实际上是一个稀疏二进制规划问题，目标函数为L0范数，约束条件为L ∞范数。然而，问题是非凸的，非光滑的，NP难的。要解决这个问题，需要进行彻底的研究.然而，所需的计算工作量太大，实际上无法实现。为了解决这些困难，我们近似的L0范数的目标函数的L1范数的目标函数，稀疏二进制规划问题的解决方案是通过应用零和一量化相应的连续值L1范数优化问题的解决方案。由于对大多数实际信号来说，等距条件是满足的，而且IMF的数目很少，所以这种近似是有效的，并通过我们对实际数据进行的实验进行了验证。由于L1范数优化问题可以转化为线性规划问题，并且许多有效的算法如单纯形法或内点法可以用于求解线性规划问题，所以我们提出的方法可以真实的实时实现。此外，与以前报道的技术，需要前兆模型或参数规格，我们提出的自适应方法不作任何假设的原始信号的特性。因此，它可以应用于提取更一般信号的潜在趋势。实验结果表明，该方法的效果优于现有的经验模态分解、经典低通滤波和小波方法。
This paper presents a novel methodology for extracting the underlying trends of signals via a joint empirical mode decomposition (EMD) and sparse binary programming approach. The EMD is applied to the signals and the corresponding intrinsic mode functions (IMFs) are obtained. The underlying trends of the signals are obtained by the sums of the IMFs where these IMFs are either selected or discarded. The total number of the selected IMFs is minimized subject to a specification on the maximum absolute differences between the denoised signals (signals obtained by discarding the first IMFs) and the underlying trends. Since the total number of the selected IMFs is minimized, the obtained solutions are sparse and only few IMFs are selected. The selected IMFs correspond to the components of the underlying trend of the signals. On the other hand, the L∞ norm specification guarantees that the maximum absolute differences between the underlying trends and the denoised signals are bounded by an acceptable level. This forces the underlying trends to follow the global changes of the signals. As the IMFs are either selected or discarded, the coefficients are either zero or one. This problem is actually a sparse binary programming problem with an L0 norm objective function subject to an L∞ norm constraint. Nevertheless, the problem is nonconvex, nonsmooth, and NP hard. It requires an exhaustive search for solving the problem. However, the required computational effort is too heavy to be implemented practically. To address these difficulties, we approximate the L0 norm objective function by the L1 norm objective function, and the solution of the sparse binary programming problem is obtained by applying the zero and one quantization to the solution of the corresponding continuous-valued L1 norm optimization problem. Since the isometry condition is satisfied and the number of the IMFs is small for most of practical signals, this approximation is valid and verified via our experiments conducted on practical data. As the L1 norm optimization problem can be reformulated as a linear programming problem and many efficient algorithms such as simplex or interior point methods can be applied for solving the linear programming problem, our proposed method can be implemented in real time. Also, unlike previously reported techniques that require precursor models or parameter specifications, our proposed adaptive method does not make any assumption on the characteristics of the original signals. Hence, it can be applied to extract the underlying trends of more general signals. The results show that our proposed method outperforms existing EMD, classical lowpass filtering and the wavelet methods in terms of the efficacy.
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DOI：
10.2307/2981806
发表时间：
1981
期刊：
--
影响因子：
--
作者：
H. Tong
通讯作者：
H. Tong
影响因子：
1.2
作者：
Tommaso Proietti
通讯作者：
Tommaso Proietti
影响因子：
4.6
作者：
W. Melek;Ziren Lu;A. Kapps;W. Fraser
通讯作者：
W. Melek;Ziren Lu;A. Kapps;W. Fraser
影响因子：
2.5
作者：
Donoho, DL;Huo, XM
通讯作者：
Huo, XM
DOI：
10.1109/icsmc.2007.4414112
发表时间：
2007-10
期刊：
2007 IEEE International Conference on Systems, Man and Cybernetics
影响因子：
--
作者：
H. Gabbar;Akinlade Damilola;H. E. Sayed
通讯作者：
H. Gabbar;Akinlade Damilola;H. E. Sayed