Accelerated model-based T1, T2* and proton density mapping using a Bayesian approach with automatic hyperparameter estimation

Purpose: To achieve automatic hyperparameter estimation for the model-based recovery of quantitative MR maps from undersampled data, we propose a Bayesian formulation that incorporates the signal model and sparse priors among multiple image contrasts.

Theory: We introduce a novel approximate message passing framework "AMP-PE" that enables the automatic and simultaneous recovery of hyperparameters and quantitative maps.

Methods: We employed the variable-flip-angle method to acquire multi-echo measurements using gradient echo sequence. We explored undersampling schemes to incorporate complementary sampling patterns across different flip angles and echo times. We further compared AMP-PE with conventional compressed sensing approaches such as the $l_1$ -norm minimization, PICS and other model-based approaches such as GraSP, MOBA.

Results: Compared to conventional compressed sensing approaches such as the $l_1$ -norm minimization and PICS, AMP-PE achieved superior reconstruction performance with lower errors in $T_2^{\ast }$ mapping and comparable performance in $T_1$ and proton density mappings. When compared to other model-based approaches including GraSP and MOBA, AMP-PE exhibited greater robustness and outperformed GraSP in reconstruction error. AMP-PE offers faster speed than MOBA. AMP-PE performed better than MOBA at higher sampling rates and worse than MOBA at a lower sampling rate. Notably, AMP-PE eliminates the need for hyperparameter tuning, which is a requisite for all the other approaches.

Conclusion: AMP-PE offers the benefits of model-based recovery with the additional key advantage of automatic hyperparameter estimation. It works adeptly in situations where ground-truth is difficult to obtain and in clinical environments where it is desirable to automatically adapt hyperparameters to individual protocol, scanner and patient.