In this paper, we conduct an investigation of the null hypothesis distribution for functional magnetic resonance imaging (fMRI) data using multiscale analysis. Most current approaches to the analysis of fMRI data assume temporal independence, or, at best, simple models for temporal (short term or long term) dependence structure. The spatial structure of fMRI data is commonly assumed to be independent or weakly spatially dependent. Such simplifications are to some extent necessary due to the complex, high-dimensional nature of the data, but to date there has been no systematic study of the dependence structures under a range of possible null hypotheses, using data sets gathered specifically for that purpose. We aim to address some of these issues by removing spatial dependence using Principal Component Analysis and analyzing the detrended data with a long enough time horizon to study possible long-range temporal dependence. We find that there is a low-dimensional spatially covarying subspace in the data that may be removed to eliminate voxel-voxel covariance in the data. Our multiscale approach using SiZer (Significance of Zero crossings of the derivative) and wavelets shows that even for resting data, i.e. "null" or ambient thought, some voxel time series cannot be modeled by white noise and need long-range dependent type error structure, while for other voxels white noise is a reasonable assumption.
Do Different Parts of the Brain Have the Same Dependence Structure? A Multiscale Analysis of the Temporal and Spatial Characteristics of Resting fMRI Data