Joint Total Variation ESTATICS for Robust Multi-Parameter Mapping

Quantitative magnetic resonance imaging (qMRI) derives tissue-specific parameters – such as the apparent transverse relaxation rate \\(R_2^\\star \\), the longitudinal relaxation rate \\(R_1\\) and the magnetisation transfer saturation – that can be compared across sites and scanners and carry important information about the underlying microstructure. The multi-parameter mapping (MPM) protocol takes advantage of multi-echo acquisitions with variable flip angles to extract these parameters in a clinically acceptable scan time. In this context, ESTATICS performs a joint loglinear fit of multiple echo series to extract \\(R_2^\\star \\) and multiple extrapolated intercepts, thereby improving robustness to motion and decreasing the variance of the estimators. In this paper, we extend this model in two ways: (1) by introducing a joint total variation (JTV) prior on the intercepts and decay, and (2) by deriving a nonlinear maximum a posteriori estimate. We evaluated the proposed algorithm by predicting left-out echoes in a rich single-subject dataset. In this validation, we outperformed other state-of-the-art methods and additionally showed that the proposed approach greatly reduces the variance of the estimated maps, without introducing bias.