Uncertainty quantification of synchrosqueezing transform under complicated nonstationary noise

2025-06-01

AI Summary

This study addresses oscillatory signals with time-varying amplitude/frequency contaminated by complex nonstationary noise. We propose the first systematic quantification of statistical uncertainty in time–frequency representations (TFRs) obtained via short-time Fourier transform (STFT)-based synchrosqueezing transform (SST). Our method introduces a Gaussian autoregressive bootstrap framework under a local stationarity assumption, grounded in a newly established Gaussian approximation theory for nonstationary stochastic process sequences. This approach overcomes classical stationarity constraints and rigorously proves SST’s robustness against nonstationary noise, enabling pointwise, interpretable TFR confidence assessment. Validation on synthetic signals and real EEG sleep spindle data demonstrates high accuracy in uncertainty estimation and strong computational feasibility. The method significantly enhances the reliability of SST-based analysis in noise-sensitive applications such as neuroscience.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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.

Problem

• Quantify uncertainty in synchrosqueezing transform with nonstationary noise
• Develop bootstrap algorithm for time-frequency representation uncertainty
• Analyze robustness of SST-based signal decomposition under noise

Innovation

• Bootstrapping algorithm for SST uncertainty quantification
• High-dimensional Gaussian approximation technique
• Gaussian auto-regressive bootstrap framework