A Proper Strucutred Prior for Bayesian T1 Mapping

Disi Lin, Anders Garpebring, Tommy Löfstedt

Keywords: Bayesian inference · T1 Mapping · Uncertainty quantification · Structured prior · Total variation.

Abstract:

This work proposes a structured prior integrated within the
Bayesian framework for variable flip angle T1 mapping. The proposed
structured prior combines total variation (TV) and ℓ1 norm functions,
and is proven to be a proper prior. The TV–ℓ1 prior promotes sparsity in
the spatial gradients of the parametric maps, resulting in smooth and coherent
image reconstructions. Embedding the prior within the Bayesian
framework enables uncertainty quantification for both T1 and M0 estimates.
Posterior inference was performed using the No-U-Turn Sampler
(NUTS). The proposed method is compared to maximum likelihood estimation
and to alternative Bayesian models that employ uniform, Laplace,
and bounded TV priors. The results show that the proposed method
yields narrower probability density functions, indicating reduced uncertainty.
The proposed method also achieves lower variance and exhibits a
smaller negative bias, reflecting more stable estimates. Overall, the integration
of TV and ℓ1 functions in a prior within the Bayesian framework
enhances spatial coherence in T1 mapping and delivers improved uncertainty
quantification, making it a promising tool for robust quantitative
MRI parameter estimation.

Submission Number: 21