Abstract
The uncertainty of reconstructed PET images remains difficult to assess and to interpret for the use in diagnostic and quantification tasks. Here we provide (1) an easy-to-use methodology for uncertainty assessment for almost any Bayesian model in PET reconstruction from single datasets and (2) a detailed analysis and interpretation of produced posterior image distributions. We apply a recent posterior bootstrap framework to the PET image reconstruction inverse problem and obtain simple parallelizable algorithms based on random weights and on existing maximum a posteriori (MAP) (posterior maximum) optimization-based algorithms. Posterior distributions are produced, analyzed and interpreted for several common Bayesian models. Their relationship with the distribution of the MAP image estimate over multiple dataset realizations is exposed. The coverage properties of posterior distributions are validated. More insight is obtained for the interpretation of posterior distributions in order to open the way for including uncertainty information into diagnostic and quantification tasks.
Highlights
In PET (Positron Emission Tomography) medical imaging, the raw data acquired by the scanner have a low SNR (Signal to Noise Ratio) and the noise is of Poisson type
Characteristics of posterior distributions We explore and present the characteristics of posterior distributions, as well as their relationship with the distribution of the corresponding MAP solution over dataset realizations
The quantitative difference is low. This is due to the convexity and to a degree of symmetry of posterior distributions for the Bayesian models used here
Summary
In PET (Positron Emission Tomography) medical imaging, the raw data acquired by the scanner have a low SNR (Signal to Noise Ratio) and the noise is of Poisson type. The image reconstruction inverse problem is ill-posed. Standard PET image reconstruction methods model the noise and use some type of spatial regularization to mitigate the noise propagation from the data to the image (Qi and Leahy 2006). The reconstruction procedure produces a single image estimate, which depends on the reconstruction method used and on the tuning of method parameters. Any subsequent visual or quantitative analysis, depend on the given noisy dataset and on the characteristics of the chosen reconstruction method. There is a need for assessing the uncertainty of voxel values in reconstructed PET image estimates
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