标题： 复杂非平稳噪声下同步挤压变换的不确定性量化 显示英文标题

标题： Uncertainty quantification of synchrosqueezing transform under complicated nonstationary noise

摘要： 我们提出了一种自助法（bootstrapping）算法，用于量化由基于短时傅里叶变换（STFT）的同步挤压变换（SST）生成的时间-频率表示（TFR）的不确定性，当输入信号是具有时变振幅和频率的振荡信号，并且受到复杂非平稳噪声污染时。 为此，我们利用最近开发的一种高维高斯近似技术，在温和假设下建立了一个非平稳随机过程的序贯高斯近似。这一结果本身具有独立的兴趣，并使我们能够量化由STFT引起的时频域随机场的近似高斯性。 在此基础上，我们在存在非平稳噪声的情况下建立了基于SST的信号分解的鲁棒性。此外，在假设噪声是局部平稳的条件下，我们开发了用于通过SST获得的TFR不确定性量化的一个高斯自回归自助框架，并提供了理论上的合理性。 我们通过模拟示例验证了所提出的算法，并通过分析脑电图记录中的纺锤波活动展示了其效用。 显示英文摘要

摘要： We propose a bootstrapping algorithm to quantify the uncertainty of the time-frequency representation (TFR) generated by the short-time Fourier transform (STFT)-based synchrosqueezing transform (SST) when the input signal is oscillatory with time-varying amplitude and frequency and contaminated by complex nonstationary noise. To this end, we leverage a recently developed high-dimensional Gaussian approximation technique to establish a sequential Gaussian approximation for nonstationary random processes under mild assumptions. This result is of independent interest and enables us to quantify the approximate Gaussianity of the random field over the time-frequency domain induced by the STFT. Building on this foundation, we establish the robustness of SST-based signal decomposition in the presence of nonstationary noise. Furthermore, under the assumption that the noise is locally stationary, we develop a Gaussian auto-regressive bootstrap framework for uncertainty quantification of the TFR obtained via SST and provide a theoretical justification. We validate the proposed method through simulated examples and demonstrate its utility by analyzing spindle activity in electroencephalogram recordings.