Wavelet variance components in image space for spatiotemporal neuroimaging data

Neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model. This allows inferences to be made about the signal estimates and resulting conclusions to be drawn about the underlying data. It can often be advantageous to interrogate temporal models after spatial transformation of the data into the wavelet domain. Wavelet bases provide a multiresolution decomposition of the spatial data dimension and an ensuing reduction in spatial correlation. However, widespread acceptance of these wavelet techniques has been hampered by the limited ability to reconstruct both parametric and error estimates into the image domain after analysis of temporal models in the wavelet domain. This paper introduces a derivation and a fast implementation of a method for the calculation of the variance of the parametric images obtained from wavelet filters. The technique is proposed for a class of estimators that have been shown to be useful in neuroimaging studies. The techniques are demonstrated for both functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) data sets.