Eigenvalue Signatures Reveal Residual Motion Effects Across Resting-State fMRI Denoising Strategies

The eigenvalue structure of resting-state fMRI (RS-fMRI) signals provides a compact representation of its variance-covariance structure, yet the information it encodes remains unclear. In this study, we introduce an eigenvalue-based framework to characterize RS-fMRI data using two features derived from the eigenspectrum: the log10-transformed first eigenvalue (log10(λ1)) and the slope of the log10-transformed spectrum (β). We systematically evaluated these features across 14 denoising strategies using two independent datasets (China167 (83 males, 84 females; mean age +/- SD: 41 +/- 14 years old) and HCP1200 (425 males, 501 females; mean age +/- SD: 29 +/- 4 years old)). Specifically, we used singular value decomposition to obtain the eigenspectrum of the cortical BOLD signals after preprocessing and nuisance regression, and a linear model to parameterize it. We then examined the relationships between the eigenvalue parameters, head motion, and functional connectivity metrics across subjects and denoising strategies. Our key findings include: (1) log10(λ1) and β strongly covaried with one another across subjects, denoising strategies, and datasets, indicating that they capture highly coherent aspects of the eigenspectrum; (2) both features were systematically influenced by denoising strategies; (3) within each denoising strategy, participants with greater log10(λ1) had greater mean framewise displacements (mFD), demonstrating sensitivity to residual motion effects, for all strategies in HCP1200 and 12/14 in China167; (4) across denoising strategies, mean log10(λ1) reflected the proportion of functional connectivity edges significantly associated with motion, indicating that higher log10(λ1) reflects more widespread motion-related contamination across large-scale functional networks; and (5) global signal regression consistently reduced log10(λ1), whereas spike regression had dataset-dependent effects. Together, these results establish eigenvalue signatures as robust and sensitive metrics for quantifying residual motion effects in RS-fMRI and provide a framework for evaluating denoising performance based on eigenvalue structure. The full procedure is implemented in R, and the corresponding script is available at: https://github.com/lejianhuang/EigenvalueSignature.