Despite the continued spread of magnetic resonance imaging (MRI) methods in scientific studies and clinical diagnosis, MRI applications are mostly restricted to high-resolution modalities such as structural MRI. While perfusion MRI gives complementary information on blood flow in the brain, its reduced resolution limits its power for detecting specific disease effects on perfusion patterns. This reduced resolution is compounded by artifacts such as partial volume effects, Gibbs ringing, and aliasing, which are caused by necessarily limited k-space sampling and the subsequent use of discrete Fourier transform (DFT) reconstruction. Here, a Bayesian modeling procedure (K-Bayes) is developed for the reconstruction of perfusion MRI. The K-Bayes approach combines a process model for the MRI signal in k-space with a Markov random field prior distribution that incorporates high-resolution segmented structural MRI information. A simulation study, described in Part I (Concepts and Applications), was performed to determine qualitative and quantitative improvements in K-Bayes reconstructed images compared with those obtained via DFT. The improvements were validated using in vivo perfusion MRI data of the human brain. The K-Bayes reconstructed images were demonstrated to provide reduced bias, increased precision, greater effect sizes, and higher resolution than those obtained using DFT.