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Bayesian Uncertainty-Aware MRI Reconstruction

Ahmed Karam Eldaly, Matteo Figini, Daniel C. Alexander

Abstract

We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior distributions are assigned to the unknown model parameters. Specifically, we assume the target image is sparse in its spatial gradient and impose a total variation prior model. A Markov chain Monte Carlo (MCMC) method, based on a split-and-augmented Gibbs sampler, is then used to sample from the resulting joint posterior distribution of the unknown parameters. Experiments conducted using single- and multi-coil datasets demonstrate the superior performance of the proposed framework over optimisation-based compressed sensing algorithms. Additionally, our framework effectively quantifies uncertainty, showing strong correlation with error maps computed from reconstructed and ground-truth images.

Bayesian Uncertainty-Aware MRI Reconstruction

Abstract

We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior distributions are assigned to the unknown model parameters. Specifically, we assume the target image is sparse in its spatial gradient and impose a total variation prior model. A Markov chain Monte Carlo (MCMC) method, based on a split-and-augmented Gibbs sampler, is then used to sample from the resulting joint posterior distribution of the unknown parameters. Experiments conducted using single- and multi-coil datasets demonstrate the superior performance of the proposed framework over optimisation-based compressed sensing algorithms. Additionally, our framework effectively quantifies uncertainty, showing strong correlation with error maps computed from reconstructed and ground-truth images.
Paper Structure (8 sections, 9 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 8 sections, 9 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Hierarchical Bayesian Model
  4. Bayesian Inference
  5. Experiments and Results
  6. Results using single-coil data
  7. Results using multi-coil data
  8. Conclusion

Figures (4)

  • Figure 1: Results of (a) image reconstruction of a brain test image from HCP data set using the four tested methods at increasing under-sampling ratio.
  • Figure 2: Error map images computed between ground truth and image estimates in Fig. \ref{['fig:MMSEEstimates']}.
  • Figure 3: Marginal standard deviation of the MCMC-TV estimates in Fig. \ref{['fig:MMSEEstimates']}.
  • Figure 4: Results of reconstruction of three brain test images from the real low-field MRI M4Raw using multicoil data at 20% under-sampling ratio.