Maximum likelihood estimators in magnetic resonance imaging

Images of the MRI signal intensity are normally constructed by taking the magnitude of the complex-valued data. This results in a biased estimate of the true signal intensity. We consider this as a problem of parameter estimation with a nuisance parameter. Using several standard techniques for this type of problem, we derive a variety of estimators for the MRI signal, some previously published and some novel. Using Monte Carlo experiments we compare the estimators we derive with others previously published. Our results suggest that one of the novel estimators we derive may strike a desirable trade-off between bias and mean squared error.