PiPs: A Kernel-based Optimization Scheme for Analyzing Non-Stationary 1D Signals
PiPs: A Kernel-based Optimization Scheme for Analyzing Non-Stationary 1D Signals
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DOI：
10.1016/j.acha.2023.04.002
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发表时间：
2018-05
影响因子：
2.5
通讯作者：
Jieren Xu;Yitong Li;Haizhao Yang;D. Dunson;I. Daubechies
中科院分区：
文献类型：
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作者：
Jieren Xu;Yitong Li;Haizhao Yang;D. Dunson;I. Daubechies
本文提出了一种新的基于核的优化方案来处理分析中的任务，例如，一维非平稳振荡信号谱估计和单通道源分离我们的优化方案重建的时间-频率信息的关键见解是，当一个非参数回归应用于一些输入值，输出回归点将位于附近的振荡模式的振荡1D信号，只有当这些输入值是一个很好的近似的地面实况相位函数。在这项工作中，高斯过程（GP）被选择来进行这种非参数回归：振荡模式被编码为模式诱导点（PiP），其作为GP回归中的训练数据点;而目标相位函数被馈入以计算相关核，作为测试输入。更好的近似相位函数生成更精确的核，从而在将基于核的回归输出与原始信号进行比较时导致更小的优化损失误差。据我们所知，这是第一个算法，可以令人满意地处理完全非平稳的振荡数据，关闭和交叉频率，和一般的振荡模式。即使在一个例子中的三角展开的参数的缓慢变化所产生的信号，我们表明，点承认竞争力或更好的性能方面的准确性和鲁棒性比现有的国家的最先进的算法。
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis,e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization scheme for reconstructing the time-frequency information is that when a nonparametric regression is applied on some input values, the output regressed points would lie near the oscillatory pattern of the oscillatory 1D signal only if these input values are a good approximation of the ground-truth phase function. In this work,Gaussian Process (GP)is chosen to conduct this nonparametric regression: the oscillatory pattern is encoded as thePattern-inducing Points (PiPs)which act as the training data points in the GP regression; while the targeted phase function is fed in to compute the correlation kernels, acting as the testing input. Better approximated phase function generates more precise kernels, thus resulting in smaller optimization loss error when comparing the kernel-based regression output with the original signals. To the best of our knowledge, this is the first algorithm that can satisfactorily handle fully non-stationary oscillatory data, close and crossover frequencies, and general oscillatory patterns. Even in the example of a signal produced by slow variation in the parameters of a trigonometric expansion, we show that PiPs admits competitive or better performance in terms of accuracy and robustness than existing state-of-the-art algorithms.