Reconstruction, analysis and interpretation of posterior probability distributions of PET images, using the posterior bootstrap

Marina Filipović (1) , Thomas Dautremer (2) , Claude Comtat (1) , Simon Stute (3, 4) , Eric Barat (2)

1 BIOMAPS - LaBoratoire d'Imagerie biOmédicale MultimodAle Paris-Saclay
2 LM2S (CEA, LIST) - Laboratoire Modélisation et Simulation de Systèmes (CEA, LIST)
3 CRCINA - Centre de Recherche en Cancérologie et Immunologie Nantes-Angers
4 NANTES - Médecine Nucléaire - Département de Médecine Nucléaire

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.

Mots clés: Tomography; Positron emission tomography; PET; PET image reconstruction; MRI; image processing; image reconstruction inverse problem; a posteriori maximum optimization (MAP); signal processing; statistical analysis; diagnosis; Non Parametric Bayesian method; Bayesian inference; Medical imaging; Modelling; Statistical inference; parallelizable algorithm; posterior probability distribution; posterior bootstrap; uncertainty quantification; multimodal image reconstruction

Domaines: Traitement du signal et de l'image [eess.SP]; Méthodologie [stat.ME]; Applications [stat.AP]; Physique Médicale [physics.med-ph]; Calcul parallèle, distribué et partagé [cs.DC]

Marina Filipović, Thomas Dautremer, Claude Comtat, Simon Stute, Eric Barat. Reconstruction, analysis and interpretation of posterior probability distributions of PET images, using the posterior bootstrap. Physics in Medicine and Biology, 2021, 66 (12), pp.125018. ⟨10.1088/1361-6560/ac06e1⟩. ⟨hal-03321853⟩