Seminars

In functional magnetic resonance imaging, the process of determining statistically significant brain activation is commonly performed in terms of (magnitude-only) voxel time course measurements after image reconstruction. The image reconstruction and statistical activation processes are treated separately. In this talk, the relationship between complex-valued (Fourier)  encoded k-space measurements and complex-valued
image measurements from (Fourier) reconstructed images is described. The voxel time-series measurements are written in terms of spatio-temporal k-space measurements. Voxel fMRI activation can be determined in image space for example using the Rowe-Logan complex-valued activation model in
terms of the original k-space measurements. Additionally, the
spatio-temporal covariance between reconstructed complex-valued voxel time series can be written in terms of the spatio-temporal covariance between complex-valued k-space measurements. Knowledge of the relationship between the spatio-temporal k-space measurements can be modeled in the more naturally acquired state rather than in a transformed state. This allows for the partitioning of the covariance matrix between the k-space measurements and hence voxel measurements into sources of covariation. Statistical associations between individual voxels or regions of interest can be quantified utilizing unmodeled sources of covariation.