  The quantification of myocardial perfusion MRI has the potential to provide a
fast, automated and user-independent assessment of myocardial ischaemia.
However, due to the relatively high noise level and low temporal resolution of
the acquired data and the complexity of the tracer-kinetic models, the model
fitting can yield unreliable parameter estimates. A solution to this problem is
the use of Bayesian inference which can incorporate prior knowledge and improve
the reliability of the parameter estimation. This, however, uses Markov chain
Monte Carlo sampling to approximate the posterior distribution of the kinetic
parameters which is extremely time intensive. This work proposes training
convolutional networks to directly predict the kinetic parameters from the
signal-intensity curves that are trained using estimates obtained from the
Bayesian inference. This allows fast estimation of the kinetic parameters with
a similar performance to the Bayesian inference.
