Statistical analysis of functional MRI data in the wavelet domain

Abstract

Abstract-The use of the wavelet transform is explored for the detection of differences between brain functional magnetic resonance images (fMRI's) acquired under two different experimental conditions. The method benefits from the fact that a smooth and spatially localized signal can be represented by a small set of localized wavelet coefficients, while the power of white noise is uniformly spread throughout the wavelet space. Hence, a statistical procedure is developed that uses the imposed decomposition orthogonality to locate wavelet-space partitions with large signal-to-noise ratio (SNR), and subsequently restricts the testing for significant wavelet coefficients to these partitions. This results in a higher SNR and a smaller number of statistical tests, yielding a lower detection threshold compared to spatial-domain testing and, thus, a higher detection sensitivity without increasing type I errors. The multiresolution approach of the wavelet method is particularly suited to applications where the signal bandwidth and/or the characteristics of an imaging modality cannot be well specified. The proposed method was applied to compare two different fMRI acquisition modalities. Differences of the respective useful signal bandwidths could be clearly demonstrated; the estimated signal, due to the smoothness of the wavelet representation, yielded more compact regions of neuroactivity than standard spatial-domain testing.

Wavelet-based multi-resolution statistics for optical imaging signals: Application to automated detection of odour activated glomeruli in the mouse olfactory bulb

“…The wavelet decomposition has been used before for the analysis of neuro-imaging data; in particular, for PET and fMRI (see Ruttimann et al, 1998;Turkheimer et al, 2000;Bullmore et al, 2003;Van De Ville et al, 2006 for an overview). An important advantage of the present framework (Van De Ville et al, 2004) is that it allows us to put the statistical test in the spatial domain.…”

Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping

“…As an alternative to GRFT, spatial wavelet transforms have been proposed as a means to non-linearly denoise functional data within frameworks of both classical inference (e.g., Aston et al, 2005;Ruttimann et al, 1998;Soleymani et al, 2009;Van De Ville et al, 2004, 2007Wink and Roerdink, 2004) and Bayesian inference (e.g., Flandin and Penny, 2007;Sanyal and Ferreira, 2012). Since brain activity is highly localized in space (Bullmore et al, 2004), the property of sparse signal representation in the wavelet domain makes it possible to encode a cluster of active voxels with only a few coefficients.…”

Spatiotemporal wavelet analysis for functional MRI

“…Our approach can be most closely compared to the work of Ruttiman et al (1998) who developed thresholding methods for fMRI based on hypothesis testing. The wavelet expansion coefficients were classified according to the validity of the nullhypothesis for each, and on this basis either selected for use in the reconstructed activation map or discarded.…”

“…In the functional MRI literature, Brammer (1998) and Ruttiman et al (1998) have used the good spatial localization properties of wavelets to better characterize fMRI activation maps. Temporal applications of wavelets in fMRI have included Bullmore et al (2002) who utilized the decorrelating properties of wavelets to control Type-1 error.…”