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SUMMARY:Variational analysis of a dynamic PET reconstruction model with op
timal transport regularization
DTSTART;VALUE=DATE-TIME:20210923T101000Z
DTEND;VALUE=DATE-TIME:20210923T103000Z
DTSTAMP;VALUE=DATE-TIME:20211201T184938Z
UID:indico-contribution-857@conference2.aau.at
DESCRIPTION:Speakers: Marco Mauritz (University of Münster\, Institute fo
r Analysis and Numerics)\nWe consider the dynamic Positron Emission Tomogr
aphy (PET) reconstruction method proposed by Schmitzer et al. $[1]$ that p
articularly 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 Benam
our-Brenier functional - over the space of positive Radon measures. This c
hoice of the regularization ensures temporal consistency between different
time points. \n\nThe PET measurements in our forward model are described
by Poisson point processes with a given intensity $q_n$. In the talk we sh
ow $\\Gamma$-convergence of the stochastic functionals $\\mathcal{E}_n$ to
a deterministic limit functional for $q_n\\to \\infty$. This helps unders
tanding the properties of the considered reconstruction method for an incr
easing 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 approxim
ation of arbitrary Radon measures by ones satisfying the continuity equati
on while controlling the Benamou-Brenier energy.\n\nReference:\n$[1]$ B. S
chmitzer\, K. P. Schäfers\, and B. Wirth. Dynamic Cell Imaging in PET wit
h\nOptimal Transport Regularization. IEEE Transactions on Medical Imaging\
,\n2019.\n\nhttps://conference2.aau.at/event/62/contributions/857/
LOCATION:Alpen-Adria-Universität Klagenfurt HS 1
URL:https://conference2.aau.at/event/62/contributions/857/
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