Uncertainty quantification of synchrosqueezing transform under complicated nonstationary noise

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.