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This study introduces bootstrap Monte Carlo singular spectrum analysis (BMC-SSA), a new method for reconstructing brain dynamics from noisy, short neuroimaging recordings like fMRI data. The technique combines statistical resampling with signal processing to identify and retain only reproducible oscillatory patterns while filtering out noise and artifacts. Testing on fMRI data demonstrates that BMC-SSA produces more reliable measurements of brain dynamics and improves the stability of mathematical models used to study complex neural activity patterns.
Why it matters
This method addresses a fundamental challenge in neuroimaging research where data quality limitations have hindered accurate analysis of brain dynamics. The approach could enable more reliable insights from existing fMRI studies and may be applicable to other fields dealing with noisy time-series data, including climate science, economics, and engineering systems.
arXiv:2510.00011v2 Announce Type: replace
Abstract: Reconstructing latent state-space geometry from time series provides a powerful route to studying nonlinear dynamics across complex systems. Delay-coordinate embedding provides the theoretical basis but assumes long, noise-free recordings, which many domains violate. In many real-world domains, recordings are short, noisy, and coarsely sampled; in neuroimaging, for example, fMRI additionally contains autocorrelated background structure that can obscure oscillatory components and destabilize embeddings. We propose bootstrap Monte Carlo singular spectrum analysis (BMC-SSA), which combines Monte Carlo SSA with bootstrap stability to retain oscillatory modes that are statistically supported and reproducible across resampled data. This produces reconstructions that emphasize reliable oscillatory structure, enhancing determinism and stabilizing subsequent embeddings. Our results show that BMC-SSA improves the reliability of functional measures and uncovers differences in state-space dynamics in fMRI, offering a general framework for robust embedding of noisy, finite signals.
Source: Robust State-space Reconstruction of Brain Dynamics via Bootstrap Monte Carlo SSA