Convergence of a data-driven time-frequency analysis method
Convergence of a data-driven time-frequency analysis method
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DOI：
10.1016/j.acha.2013.12.004
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
T. Hou;Zuoqiang Shi;P. Tavallali
中科院分区：
文献类型：
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作者：
T. Hou;Zuoqiang Shi;P. Tavallali
摘要 在最近的一篇论文[11]中，Hou 和 Shi 介绍了一种新的自适应数据分析方法来分析非线性和非平稳数据。主要思想是在由 {a (t) cos (θ (t))} 形式的本征模态函数组成的最大可能字典中寻找多尺度数据的最稀疏表示，其中 a∈ V (θ)、V (θ) 由比 cos (θ (t)) 和 θ′⩾ 0 振荡更小的函数组成。该问题被表述为非线性 L 0 优化问题，并提出了迭代非线性匹配追踪方法来解决该非线性优化问题。在本文中，我们证明了这种非线性匹配追踪方法在信号的某些尺度分离假设下的收敛性。我们考虑分辨率良好和采样不良的信号，以及带有噪声的信号。在没有噪声的情况下，我们证明我们的方法可以准确恢复原始信号。
Abstract In a recent paper [11], Hou and Shi introduced a new adaptive data analysis method to analyze nonlinear and non-stationary data. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a (t) cos (θ (t))}, where a∈ V (θ), V (θ) consists of the functions that are less oscillatory than cos (θ (t)) and θ′⩾ 0. This problem was formulated as a nonlinear L 0 optimization problem and an iterative nonlinear matching pursuit method was proposed to solve this nonlinear optimization problem. In this paper, we prove the convergence of this nonlinear matching pursuit method under some scale separation assumptions on the signal. We consider both well-resolved and poorly sampled signals, as well as signals with noise. In the case without noise, we prove that our method gives exact recovery of the original signal.