Methods for Uncertainty Quantification in Dictionary Matching to Advance Reliability of Quantitative MRI

Purpose: Dictionary matching is a standard tool in quantitative MRI (qMRI), but typically lacks uncertainty quantification (UQ). This is critical when advanced reconstructions (e.g., compressed sensing, deep learning) introduce complex-valued, spatially varying, and temporally correlated noise that violates standard assumptions of independent and identically distributed (iid) noise.

Two voxel-wise uncertainty methods: a frequentist Likelihood Ratio Test (LRT) and a Bayesian marginal posterior approach, are introduced. Noise is modeled as spatially varying and temporally correlated using the covariance estimated from background regions. Methods were validated via simulations and phantom experiments using radial turbo spin-echo ( $T_2$ mapping) and radial Look-Locker ( $T_1$ mapping). In vivo experiments characterized uncertainty under varying acceleration factors.

Simulations confirmed both methods achieve nominal coverage rates (e.g., 95% intervals containing the true value 95% of the time) where standard iid assumptions fail. Phantom results showed excellent agreement with gold-standard spin-echo references. In vivo experiments highlighted that higher acceleration factors widen uncertainty intervals for $T_1$ and $T_2$ . The LRT method proved more computationally efficient than the Bayesian approach while providing comparable interval estimates.

A robust framework is presented for UQ in dictionary-matched qMRI. By modeling the non-iid noise inherent in modern reconstructions, these methods provide statistically interpretable UQ that assesses the reliability of parameter maps in clinical settings.