PET image reconstruction and motion correction using direct backprojection on point grids and clouds

PET and SPECT images are traditionally reconstructed using voxel grids. In situations where non-rigid motion correction is required, meshes are believed to be better suited than voxels for image reconstruction. With meshes, deformations can be modeled explicitly by changing the coordinates of the mesh nodes. Previously proposed approaches to mesh-based image reconstruction relied either on computing the projection of mesh polyhedrons onto the detector planes, or computing the length-of-intersection between the polyhedrons and the lines-of-response. We propose and validate new approaches to analytic and iterative PET image reconstruction that employs regular and irregular point sets. Within the proposed methods, the topology between points is ignored, and only the distances between the lines-of-response and points are considered. This should potentially result in shorter computation times compared to the previously proposed algorithms. A new method of motion correction based on point displacement is also considered. Minimal differences were observed between images reconstructed using point grids and clouds and images obtained using the conventional, voxel-based iterative and analytical image reconstruction. This validates the proposed methods and demonstrates that the distance-based image reconstruction based on point sets can be used for quantitative PET imaging.