Spatially Compact MR-Guided Kernel EM for PET Image Reconstruction

Positron emission tomography (PET) is a highly sensitive functional and molecular imaging modality which can measure picomolar concentrations of an injected radionuclide. However, the physical sensitivity of PET is limited, and reducing the injected dose leads to low count data and noisy reconstructed images. A highly effective way of reducing noise is to reparameterize the reconstruction in terms of MR-derived spatial basis functions. Spatial basis functions derived using the kernel method have demonstrated excellent noise reduction properties and maintain shared PET-MR detailed structures. However, as previously shown in the literature, the MR-guided kernel method may lead to excessive smoothing of structures that are only present in the PET data. This paper makes two main contributions in order to address this problem: first, we exploit the potential of the MR-guided kernel method to form more spatially compact basis functions which are able to preserve PET-unique structures, and second, we consider reconstruction at the native MR resolution. The former contribution notably improves the recovery of structures which are unique to the PET data. These adaptations of the kernel method were compared to the conventional implementation of the MR-guided kernel method and also to maximum likelihood expectation maximization, in terms of ability to recover PET unique structures for both simulated and real data. The spatially compact kernel method showed clear visual and quantitative improvements in the reconstruction of the PET unique structures, relative to the conventional kernel method for all sizes of PET unique structures investigated, whilst maintaining to a large extent the impressive noise mitigating and detail preserving properties of the conventional MR-guided kernel method. We therefore conclude that a spatially compact parameterization of the MR-guided kernel method, should be the preferred implementation strategy in order to obviate unnecessary losses in PET-unique details.