Nonparametric posterior learning for emission tomography

Fedor Goncharov (1) , Eric Barat (1) , Thomas Dautremer (1)

1 LM2S (CEA, LIST) - Laboratoire Modélisation et Simulation de Systèmes (CEA, LIST)

We continue studies of the uncertainty quantification problem in emission tomographies such aspositron emission tomography (PET) or single photon emission computed tomography (SPECT)when additional multimodal data (anatomical magnetic resonance imaging (MRI) images) are avail-able. To solve the aforementioned problem we adapt the recently proposed nonparametric posteriorlearning technique to the context of Poisson-type data in emission tomography. Using this approachwe derive sampling algorithms which are trivially parallelizable, scalable and very easy to implement.In addition, we prove conditional consistency and tightness for the distribution of produced samplesin the small noise limit (i.e., when the acquisition time tends to infinity) and derive new geometricaland necessary condition on how MRI images must be used. This condition arises naturally in thecontext of identifiability problem for misspecified generalized Poisson models with wrong design. Wealso contrast our approach with Bayesian Markov chain Monte Carlo sampling based on one dataaugmentation scheme which is very popular in the context of expectation-maximization algorithmsfor PET or SPECT. We show theoretically and also numerically that such data augmentation sig-nificantly increases mixing times for the Markov chain. In view of this, our algorithms seem to givea reasonable trade-off between design complexity, scalability, numerical load and assessment for theuncertainty

Keywords: tomography; inverse problems; MCMC; Bayesian inference; bootstrap; signal processing; Non Parametric Bayesian method; Statistical inference; Medical imaging; ionizing radiation

Domains: Statistics [math.ST]; Signal and Image Processing; Medical Physics [physics.med-ph]

Fedor Goncharov, Eric Barat, Thomas Dautremer. Nonparametric posterior learning for emission tomography. SIAM/ASA Journal on Uncertainty Quantification, 2023, 11 (2), pp.452-479. ⟨10.1137/21M1463367⟩. ⟨cea-04123345v5⟩