Parameter estimation from Rician-distributed data sets using a maximum likelihood estimator: application to T1 and perfusion measurements.

General expressions are presented to calculate the maximum likelihood (ML) estimator and corresponding Fisher matrix for Rician-distributed data sets. This estimator results in the most precise, unbiased estimations of T1 from magnitude data sets, even when low signal-to-noise ratios (<6) are present. By optimizing the sample point distributions for inversion-recovery experiments, a 32% increase in precision of the estimated T1 is obtained, compared with a linear sampling scheme. Perfusion rates are estimated from combined data sets of the slice- and nonslice-selective inversion-recovery experiments, as obtained with the flow-sensitive alternating inversion recovery (FAIR) technique. The ML estimator for the combined data set results in the most precise, unbiased estimations of the perfusion rate. Error analysis shows that very high signal-to-noise ratios are required for precise estimation of perfusion rates from FAIR experiments.