# 2nd Alps-Adriatic Inverse Problems Workshop 2021 (AAIP 2021) Chemnitz Inverse Problems Symposium on tour

22-24 September 2021
Europe/Vienna timezone

## Variational analysis of a dynamic PET reconstruction model with optimal transport regularization

23 Sep 2021, 12:10
20m
HS 1 (Alpen-Adria-Universität Klagenfurt)

### Speaker

Marco Mauritz (University of Münster, Institute for Analysis and Numerics)

### Description

We consider the dynamic Positron Emission Tomography (PET) reconstruction method proposed by Schmitzer et al. $[1]$ that particularly aims to reconstruct the temporal evolution of single or small numbers of cells by leveraging optimal transport. Using a MAP estimate the cells' evolution is reconstructed by minimizing a functional $\mathcal{E}_n$ - composed of a Kulback-Leibler-type data fidelity term and the Benamour-Brenier functional - over the space of positive Radon measures. This choice of the regularization ensures temporal consistency between different time points.

The PET measurements in our forward model are described by Poisson point processes with a given intensity $q_n$. In the talk we show $\Gamma$-convergence of the stochastic functionals $\mathcal{E}_n$ to a deterministic limit functional for $q_n\to \infty$. This helps understanding the properties of the considered reconstruction method for an increasing SNR. To compute the $\Gamma$-limit we show convergence of Poisson point processes for intensities growing to infinity as well as convergence of the optimal transport regularization. The latter requires the approximation of arbitrary Radon measures by ones satisfying the continuity equation while controlling the Benamou-Brenier energy.

Reference:
$[1]$ B. Schmitzer, K. P. Schäfers, and B. Wirth. Dynamic Cell Imaging in PET with
Optimal Transport Regularization. IEEE Transactions on Medical Imaging,
2019.

### Primary authors

Marco Mauritz (University of Münster, Institute for Analysis and Numerics) Prof. Benedikt Wirth (University of Münster, Institute for Analysis and Numerics)

### Presentation Materials

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