Maximum a posteriori estimation of diffusion tensor parameters using a Rician noise model: why, how and but.

The diffusion tensor is a commonly used model for diffusion-weighted MR image data. The parameters are typically estimated by ordinary or weighted least squares on log-transformed data, assuming normal or log-normal distribution of measurement errors respectively. This may not be adequate when using high b-values and or performing high-resolution scans, resulting in poor SNR, in which case the difference between the assumed and the true (Rician) noise model becomes important. As a consequence the estimated diffusion parameters will be biased, underestimating the true diffusion. In this paper a computational framework is presented where parameters pertaining to a spectral decomposition of the diffusion tensor are estimated using a Rician noise model. The parameters are estimated using a Fisher-scoring scheme which gives robust and rapid convergence. It is demonstrated how the Fisher-information matrix can be used as a generic tool for designing optimal experiments. It is shown that the Rician noise model leads to significantly less biased estimates for a large range of b-values and SNR, but that the Rician estimates have a poorer precision compared to the Gaussian model for very low SNR. By pooling the Rician estimates of uncertainty over neighbouring voxel estimates with higher precision, but still not as high as with a Gaussian model, can be obtained. We suggest the use of a Rician estimator when it is important with truly quantitative values and when comparing different predictive models. The higher precision of the Gaussian estimates may be more important when the objective is to compare diffusion related parameters over time or across groups.