Motion-based interpolation to estimate spatially variant PSF in Positron Emission Tomography

This paper deals with the restoration of Positron Emission Tomography images. The partial volume effect creates blurring in such images and causes inaccurate quantization. This artefact is due to the complex geometry of the acquisition system. We propose to represent this complexity by a spatially variable point spread function. The PSF is first measured at a set of locations in the field of view and estimated at any other location. Existing linear interpolation methods consider only the variability of the intensity. In order to consider shape variability of the PSF, we formulate the estimation of an unknown PSF as mass transportation problem of known PSFs. An optimal transport optimization algorithm is used to solve the problem. GATE simulations are used to evaluate the method and compare it to a PCA based approach. Application to partial volume assessment in reconstructed PET images is presented. The promising results set up the possibility to develop more robust PET image restoration.