Infimal convolution spatiotemporal PET reconstruction using total variation based priors

Maïtine Bergounioux (1) , Evangelos Papoutsellis (2) , Simon Stute (3) , Clovis Tauber (2)

1 IDP - Institut Denis Poisson
2 iBraiN - Imaging, Brain & Neuropsychiatry
3 IMIV - U1023 - ERL9218 - Imagerie Moléculaire in Vivo

In this paper, we focus on spatiotemporal regularization of Positron Emission Tomography (PET) reconstruction. Through a minimization problem defined on a dynamic variational framework we consider regularizers based on total variation priors adapted to problems related to Poisson noise degradation. In particular, we consider spatiotemporal total variation and total generalized variation and their corresponding extensions to the infimal convolution regularization. The numerical solutions of the corresponding variational problems are performed using Primal-Dual Hybrid Gradient (PDHG) optimization methods under a diagonal preconditioning. We compare our numerical solutions with the standard Maximum Likelihood Expectation Maximization (MLEM) reconstruction for simulated dynamic brain data for different kind of radiotracers. Our results indicate that the infimal convolution approaches provide better reconstructions compared to the ground truth brain phantom.

Mots clés: Total Variation; Total generalized variation; Infimal convolution; Spatiotemporal regularization; Dynamic Positron Emission Tomography; Primal-Dual Hybrid Gradient optimization methods

Domaines: Optimisation et contrôle [math.OC]; Traitement des images [eess.IV]

Maïtine Bergounioux, Evangelos Papoutsellis, Simon Stute, Clovis Tauber. Infimal convolution spatiotemporal PET reconstruction using total variation based priors. 2018. ⟨hal-01694064⟩