  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.
