  Low-count reconstruction remains a challenge for Positron Emission Tomography
(PET) even with the recent progress in time-of-flight (TOF) resolution. In this
context, the bias between the acquired histogram, consisting of low values or
zeros, and the expected histogram, obtained from the forward projector, is
propagated to the image, resulting in a biased reconstruction. This situation
could be exacerbated with finer resolution of the TOF information, which
further sparsifies the acquired histogram. We propose a new approach to
circumvent this limitation of the classical reconstruction model. It consists
of extending the description of the reconstruction scheme to also explicitly
include the projection domain by Parameterizing the Angular Distribution of
Emission (PADE). This parametrization has greater degrees of freedom than the
log-likelihood model, which can not be harnessed in classical circumstances. We
hypothesize that with ultra-fast TOF this new approach would not only be viable
for low-count reconstruction, but also more adequate than the classical
reconstruction model. As a proof of concept, an implementation of this approach
is compared to the log-likelihood model by investigating two-dimensional
simulations of a hot spots phantom. The proposed model achieves similar
contrast recovery coefficients as MLEM except for the smallest structures where
the low-count nature of the simulations makes it difficult to draw conclusions.
However, this new model seems to converge toward less noisy solutions than
MLEM. These results suggest that the PADE approach has potential for low-count
reconstruction with ultra-fast TOF.
