Bayesian Inverse Regression for Vascular Magnetic Resonance Fingerprinting

Standard parameter estimation from vascular magnetic resonance fingerprinting (MRF) data is based on matching the MRF signals to their best counterparts in a grid of coupled simulated signals and parameters, referred to as a dictionary. To reach a good accuracy, the matching requires an informative dictionary whose cost, in terms of design, storage and exploration, is rapidly prohibitive for even moderate numbers of parameters. In this work, we propose an alternative dictionary-based statistical learning (DB-SL) approach made of three steps: 1) a quasi-random sampling strategy to produce efficiently an informative dictionary, 2) an inverse statistical regression model to learn from the dictionary a correspondence between fingerprints and parameters, and 3) the use of this mapping to provide both parameter estimates and their confidence indices. The proposed DB-SL approach is compared to both the standard dictionary-based matching (DBM) method and to a dictionary-based deep learning (DB-DL) method. Performance is illustrated first on synthetic signals including scalable and standard MRF signals with spatial undersampling noise. Then, vascular MRF signals are considered both through simulations and real data acquired in tumor bearing rats. Overall, the two learning methods yield more accurate parameter estimates than matching and to a range not limited to the dictionary boundaries. DB-SL in particular resists to higher noise levels and provides in addition confidence indices on the estimates at no additional cost. DB-SL appears as a promising method to reduce simulation needs and computational requirements, while modeling sources of uncertainty and providing both accurate and interpretable results.