k-t PCA is a a regularized image reconstruction method to recover images from highly undersampled dynamic magnetic resonance data. It is based on the decomposition of the training and the undersampled data into temporally and spatially invariant terms using principal component analysis. In this paper, a compartment-based k-t PCA reconstruction approach is presented, with the objective of improving highly undersampled, high-resolution 3D myocardial perfusion magnetic resonance imaging (MRI) by constraining the temporal content of different spatial compartments in the image series based on the bolus arrival times and prior knowledge about the signal intensity-time curves.