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.