Modelling and estimation of multicomponent T2 distributions

Kelvin J. Layton, Mark Morelande, David Wright, Peter M. Farrell, Bill Moran, Leigh A. Johnston

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18 Citations (Scopus)


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 T 2 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.

Original languageEnglish
Article number6508949
Pages (from-to)1423-1434
Number of pages12
JournalIEEE Transactions on Medical Imaging
Issue number8
Publication statusPublished - 2013
Externally publishedYes


  • Extended phase graph
  • multicomponent relaxometry
  • nonnegative least squares (NNLS)
  • progressive correction
  • stimulated echo
  • T relaxation

Cite this

Layton, K. J., Morelande, M., Wright, D., Farrell, P. M., Moran, B., & Johnston, L. A. (2013). Modelling and estimation of multicomponent T2 distributions. IEEE Transactions on Medical Imaging, 32(8), 1423-1434. [6508949].