| name | fmri-mahalanobis-bures-whitening |
| description | De-individualizing fMRI signals via Mahalanobis whitening and Bures geometry — methodology for distilling meaningful information from fMRI by treating data whitening as quantum-inspired state de-individualization using Bures distance. |
| activation_keywords | ["fMRI de-individualization","Mahalanobis whitening brain","Bures distance fMRI","fMRI functional connectivity","quantum-inspired brain analysis","功能连接去个体化","fMRI白化","Bures几何脑成像","Alzheimer fMRI biomarker","functional connectivity preprocessing"] |
| categories | ["neuroscience","medical-imaging","quantum-physics"] |
| arxiv_id | 2511.07313 |
| arxiv_url | https://arxiv.org/abs/2511.07313 |
| authors | Aaron Jacobson, Tingting Dan, Martin Styner, Guorong Wu, Shahar Kovalsky, Caroline Moosmueller |
| created | 2026-06-08 |
De-Individualizing fMRI Signals via Mahalanobis Whitening and Bures Geometry
Description
Methodology for processing fMRI signals through Mahalanobis data whitening to extract meaningful information about subjects and experimental stimuli. Provides a quantum-inspired interpretation of whitening as a two-stage de-individualization process motivated by the Bures distance from quantum mechanics. Applications include improving Alzheimer's diagnosis accuracy, especially in preclinical stages.
Core Concepts
Mahalanobis Whitening for fMRI
- Standard fMRI analysis suffers from subject-specific confounds
- Mahalanobis whitening: x_whitened = Σ^(-1/2) · (x - μ)
- Removes individual covariance structure while preserving stimulus-relevant information
- Two-stage process: (1) remove subject identity, (2) preserve experimental signal
Bures Distance Connection
- Bures distance: D_B(ρ₁, ρ₂) = √[2(1 - Tr√(√ρ₁·ρ₂·√ρ₁))]
- Quantum metric for distinguishing quantum states
- Applied to fMRI covariance matrices as "quantum states" of brain activity
- Provides geometrically meaningful distance between brain states
Methodology Steps
Step 1: Compute Subject Covariance
For each subject s:
Σ_s = Cov(fMRI_time_series_s)
μ_s = Mean(fMRI_time_series_s)
Step 2: Apply Mahalanobis Whitening
Global covariance: Σ_global = Average(Σ_s) across subjects
Whitening matrix: W = Σ_global^(-1/2)
Whitened data: x' = W · (x - μ_global)
Step 3: Bures Distance Analysis
Treat each subject's covariance as density matrix: ρ_s = Σ_s / Tr(Σ_s)
Compute Bures distance between subject states:
D_B(ρ_s, ρ_t) = √[2(1 - Tr√(√ρ_s · ρ_t · √ρ_s))]
Step 4: De-Individualization Validation
- Verify that whitened data no longer encodes subject identity
- Confirm that stimulus/experimental effects are preserved
- Use cross-validation on downstream tasks (classification, prediction)
Applications
- Alzheimer's diagnosis: Improved accuracy in preclinical stage detection
- Cross-subject fMRI analysis: Remove individual confounds for group studies
- Biomarker discovery: Isolate disease-relevant signals from individual variation
- Brain-computer interfaces: Standardized features across subjects
- Longitudinal studies: Track changes within subjects over time
Key Advantages
