Modelling and Estimation of Multicomponent $T_{2}$ Distributions

Estimation of multiple T₂ components within single imaging voxels typically proceeds in one of two ways; a nonparametric grid approximation to a continuous distribution is made and a regularized nonnegative least squares algorithm is employed to perform the parameter estimation, or a parametric multicomponent model is assumed with a maximum likelihood estimator for the component estimation. In this work, we present a Bayesian algorithm based on the principle of progressive correction for the latter choice of a discrete multicomponent model. We demonstrate in application to simulated data and two experimental datasets that our Bayesian approach provides robust and accurate estimates of both the T₂ model parameters and nonideal flip angles. The second contribution of the paper is to present a Cramér-Rao analysis of T₂ component width estimators. To this end, we introduce a parsimonious parametric and continuous model based on a mixture of inverse-gamma distributions. This analysis supports the notion that T₂ spread is difficult, if not infeasible, to estimate from relaxometry data acquired with a typical clinical paradigm. These results justify the use of the discrete distribution model.