Analysis of functional magnetic resonance images by wavelet decomposition
The use of the wavelet transform to detect differences between sequentially acquired functional magnetic resonance images (fMRIs) is explored. A statistical data model is developed that makes use of the orthogonality and regularity conditions of the wavelets to achieve a signal decomposition into uncorrelated components, enabling application of standard parametric tests of significance on wavelet coefficients directly. This overcomes the problems associated with high intervoxel correlations in the spatial domain, and achieves economy in statistical testing by limiting the search for significant signal components to a subspace where the signal power is located. Thus, a smaller p-value adjustment for multiple testing is required, resulting in a lower detection threshold for a given overall level of statistical significance. For the fMRIs investigated, a 10:1 reduction in the number of statistical tests was achieved, and about 1% of the wavelet coefficients were significant (p<0.05 per volume), which then served to resynthesize the difference images by inverse wavelet transform.