A Bregman Majorization-Minimization Framework for PET Image Reconstruction

Claire Rossignol (1) , Florent Sureau (2) , Émilie Chouzenoux (1) , Claude Comtat (2) , Jean-Christophe Pesquet (1)

1 OPIS - OPtimisation Imagerie et Santé
2 BIOMAPS - LaBoratoire d'Imagerie biOmédicale MultimodAle Paris-Saclay

Positron emission tomography (PET) is a quantitative imaging modality widely used in oncology, neurology, and pharmacology. The data acquired by a PET scanner correspond to projections of the concentration activity, assumed to follow a Poisson distribution. The reconstruction of images from tomographic projections corrupted by Poisson noise is a challenging ill-posed large-scale inverse problem. Several available solvers use the majorization-minimization (MM) principle, though relying on various construction strategies with a lack of unifying framework. This work fills the gap by introducing the concept of Bregman majorization. This leads to a unified view of MM-based methods for image reconstruction in the presence of Poisson noise. From this general approach, we exhibit three algorithmic solutions and compare their computational efficiency on a problem of dynamic PET image reconstruction, either using GPU or CPU processing.

Mots clés: PET image reconstruction; Poisson noise; Majorization-Minimisation; Bregman divergence; GPU implementation

Domaines: Traitement du signal et de l'image [eess.SP]

Claire Rossignol, Florent Sureau, Émilie Chouzenoux, Claude Comtat, Jean-Christophe Pesquet. A Bregman Majorization-Minimization Framework for PET Image Reconstruction. ICIP 2022 - 29th IEEE International Conference on Image Processing, Oct 2022, Bordeaux, France. ⟨hal-03720547⟩