Wavelet methods for characterising mono- and poly-fractal noise structures in shortish time series: An application to functional MRI

Jalal M. Fadili (1) , Edward T. Bullmore (2) , Matthew Brett (3)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 Brain Mapping Unit
3 MRC CBU - Cognition and Brain Sciences Unit

Functional magnetic resonance imaging (fMRI) time series generally demonstrate serial dependence. This endogenous auto-correlation typically exhibits long-range dependence described by a 1/f -like power law. In this paper, we present a novel wavelet-based methodology for characterising the noise structure in short-medium length (shortish) fMRI time series. Mono-fractality is assessed in terms of the Hurst exponent and the noise variance. We then investigate potential local stationarity of the Hurst exponent in fMRI data and present a Uniformly Most Powerful test for its time constancy. A novel bootstrap approach is presented as an alternative to the Normal assumption and its advantages are discussed. From several datasets investigated, we specifically showthat the 1/f model is particularly suited to describe color in fMRI noise. We also demonstrate that even if most of the brain voxels are mono-fractal, there are many locations in the brain where time constancy of the Hurst exponent is violated, i.e., the noise structure is poly-fractal.

Domaines: Traitement des images [eess.IV]

Jalal M. Fadili, Edward T. Bullmore, Matthew Brett. Wavelet methods for characterising mono- and poly-fractal noise structures in shortish time series: An application to functional MRI. IEEE International Conference on Image Processing 2001, 2001, Thessaloniki, Greece. pp.225-228, ⟨10.1109/ICIP.2001.958465⟩. ⟨hal-01016058⟩