Image reconstructions from super-sampled data sets in PET imaging

Spatial resolution in positron emission tomography (PET) is still a limiting factor in many imaging applications. To improve the spatial resolution for an existing scanner with fixed crystal sizes, mechanical movements such as scanner wobbling and object shifting have been considered for PET systems. Multiple acquisitions from different positions provide both redundant and complementary information. The objective of this paper is to explore efficient and useful reconstruction framework to reconstruct super-resolution images from super-sampled low-resolution data. We first create a super-sampling data acquisition model based on the physical processes with tomographic, down-sampling and shifting matrices as its building blocks. Based on the model, we extend ML-EM and Landweber algorithms to reconstruct images from multiple data sets. We also derive a backprojection-filtration-type (BPF) method for the super-resolution reconstruction. Further, we explore variant methods for super-sampling reconstructions: the separate super-sampling resolution-modeling reconstruction and the reconstruction without down-sampling to further improve image quality at the cost of more computation. We used simulated reconstruction of a resolution phantom to evaluate the three types of algorithms with different super-samplings. Contrast recovery coefficient (CRC) versus background variability, as an image-quality metric, is calculated at each iteration. We observe that all three algorithms can significantly and consistently achieve increased CRCs and reduce background artifacts with super-sampled data sets at the same total counts. ML-EM achieves better image quality than Landweber, which in turn achieves better image quality than BPF. We also demonstrate that the reconstructions from super-sampled data sets using a fine system matrix yield improved image quality compared to the reconstructions using a coarse system matrix.