Estimating posterior image variance with sparsity-based object priors for MRI

Point estimates, such as the maximum a posteriori (MAP) estimate, are commonly computed in image re- construction tasks. However, such point estimates provide no information about the range of highly probable solutions, namely the uncertainty in the computed estimate. Bayesian inference methods that seek to compute the posterior probability distribution function (PDF) of the object can provide exactly this information, but are generally computationally intractable. Markov Chain Monte Carlo (MCMC) methods, which avoid explicit posterior computation by directly sampling from the PDF, require considerable expertise to run in a proper way. This work investigates a computationally efficient variational Bayesian inference approach for computing the posterior image variance with application to MRI. The methodology employs a sparse object prior model that is consistent with the model assumed in most sparse reconstruction methods. The posterior variance map generated by the proposed method provides valuable information that reveals how data-acquisition parameters and the specification of the object prior affect the reliability of a reconstructed MAP image. The proposed method is demonstrated by use of computer-simulated MRI data.