Functional Magnetic Resonance Imaging (fMRI) is a primary modality for studying brain activity. Modeling spatial dependence of imaging data at different scales is one of the main challenges of contemporary neuroimaging, and it could allow for accurate testing for significance in neural activity. The high dimensionality of this type of data (on the order of hundreds of thousands of voxels) poses serious modeling challenges and considerable computational constraints. For the sake of feasibility, standard models typically reduce dimensionality by modeling covariance among regions of interest (ROIs) -- coarser or larger spatial units -- rather than among voxels. However, ignoring spatial dependence at different scales could drastically reduce our ability to detect activation patterns in the brain and hence produce misleading results. To overcome these problems, we introduce a multi-resolution spatio-temporal model and a computationally efficient methodology to estimate cognitive control related activation and whole-brain connectivity. The proposed model allows for testing voxel-specific activation while accounting for non-stationary local spatial dependence within anatomically defined ROIs, as well as regional dependence (between-ROIs). Furthermore, the model allows for detection of interpretable connectivity patterns among ROIs using the graphical Least Absolute Shrinkage Selection Operator (LASSO). The model is used in a motor-task fMRI study to investigate brain activation and connectivity patterns aimed at identifying associations between these patterns and regaining motor functionality following a stroke.
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