Time Shifted Principle Component Analysis

Jason K. Mendes¹, Dennis L. Parker¹

The temporal signal in any given voxel can be approximated by a combination of a finite number of basis functions (or principle components). As we keep fewer principle components, we can increase the amount of data undersampling. This can cause a problem, however, when two voxels exhibit highly correlated signals that differ by only a small delay in time. In such cases, keeping only a small number of principle components can inadvertently change the temporal characteristics of these voxels by matching them to the same principle components. The proposed method helps to address this concern by reducing the number of principle components needed to reconstruct an undersampled data set by allowing time shifted principle components.