On The Local Geometry of the Pet Reconstruction Problem

Intrinsic uncertainties related to the ill-posedness of the PET reconstruction problem are investigated in this work. These uncertainties could lead to artifacts in the reconstructed images in particular when Deep Learning approaches are employed. We propose a framework enabling to define a distinguishability measure between PET images and propose a local analysis of such a measure in a neighborhood of a reference image. This approach is numerically tested on a synthetic experiment using a 3D brain PET phantom derived from a [18F]-FDG exam with 100 anatomo-functional regions extracted. Our analysis allows us to highlight the key factors impacting the detectability of variations and to exhibit concrete examples of clinically meaningful directions along which variations may not be detectable. In addition, we quantitatively analyze the role played by the injected radiotracer dose and show that low-dose scenarios are particularly prone to the presence of reconstruction artifacts.