Bayesian non-linear regression with spatial priors for noise reduction and error estimation in quantitative MRI with an application in T1 estimation. (19th November 2020)

• Record Type: Journal Article
• Authors: Löfstedt, Tommy; Hellström, Max; Bylund, Mikael; Garpebring, Anders
• Is Part Of: Physics in medicine & biology. Volume 65:Number 22(2020:Nov.)
• Publication Date: 2020-11-19
• Subjects: Bayesian statistics -- quantitative MRI -- noise reduction -- tissue parameter estimation -- WAIC; Biophysics -- Periodicals; Medical physics -- Periodicals; 610.153
• DOI: 10.1088/1361-6560/abb9f5
• Languages: English
• ISSNs: 0031-9155

Abstract

Abstract: Purpose. To develop a method that can reduce and estimate uncertainty in quantitative MR parameter maps without the need for hand-tuning of any hyperparameters. Methods. We present an estimation method where uncertainties are reduced by incorporating information on spatial correlations between neighbouring voxels. The method is based on a Bayesian hierarchical non-linear regression model, where the parameters of interest are sampled, using Markov chain Monte Carlo (MCMC), from a high-dimensional posterior distribution with a spatial prior. The degree to which the prior affects the model is determined by an automatic hyperparameter search using an information criterion and is, therefore, free from manual user-dependent tuning. The samples obtained further provide a convenient means to obtain uncertainties in both voxels and regions. The developed method was evaluated on T 1 estimations based on the variable flip angle method. Results. The proposed method delivers noise-reduced T 1 parameter maps with associated error estimates by combining MCMC sampling, the widely applicable information criterion, and total variation-based denoising. The proposed method results in an overall decrease in estimation error when compared to conventional voxel-wise maximum likelihood estimation. However, this comes with an increased bias in some regions, predominately at tissue interfaces, as well as an increase in computational time. Conclusions. This study provides a method that generates more precise estimates compared to the conventional method, without incorporating user subjectivity, and with the added benefit of uncertainty estimation.