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Low-count reconstruction remains a challenge for Positron Emission Tomography(PET) even with the recent progress in time-of-flight (TOF) resolution. In thiscontext, the bias between the acquired histogram, consisting of low values orzeros, and the expected histogram, obtained from the forward projector, ispropagated to the image, resulting in a biased reconstruction. This situationcould be exacerbated with finer resolution of the TOF information, whichfurther sparsifies the acquired histogram. We propose a new approach tocircumvent this limitation of the classical reconstruction model. It consistsof extending the description of the reconstruction scheme to also explicitlyinclude the projection domain by Parameterizing the Angular Distribution ofEmission (PADE). This parametrization has greater degrees of freedom than thelog-likelihood model, which can not be harnessed in classical circumstances. Wehypothesize that with ultra-fast TOF this new approach would not only be viablefor low-count reconstruction, but also more adequate than the classicalreconstruction model. As a proof of concept, an implementation of this approachis compared to the log-likelihood model by investigating two-dimensionalsimulations of a hot spots phantom. The proposed model achieves similarcontrast recovery coefficients as MLEM except for the smallest structures wherethe low-count nature of the simulations makes it difficult to draw conclusions.However, this new model seems to converge toward less noisy solutions thanMLEM. These results suggest that the PADE approach has potential for low-countreconstruction with ultra-fast TOF.

Parameterizing the Angular Distribution of Emission: A Model for TOF-PET Low-Count Reconstruction