Efficient 3D grids for image reconstruction using spherically-symmetric volume elements

Incorporation of spherically-symmetric volume elements (blobs), instead of the conventional voxels, into iterative image reconstruction algorithms, has been found in our previous studies to lead to significant improvement in the quality of the reconstructed images. Furthermore, for three-dimensional (3D) positron emission tomography the 3D algebraic reconstruction technique using blobs can reach comparable or even better quality than the 3D filtered backprojection method after only one cycle through the projection data. The only shortcoming of the blob reconstruction method is an increased computational demand, because of the overlapping nature of the blobs. In our previous studies the blobs were placed on the same 3D simple cubic grid as used for voxel basis functions. For spherically-symmetric basis functions there are more advantageous arrangements of the 3D grid, enabling a more isotropic distribution of the spherical functions in the 3D space and a better packing efficiency of the image spectrum. Our studies confirmed that, when using the body centered cubic grid, the number of grid points can be effectively reduced, decreasing the computational and memory demands while preserving the quality of the reconstructed images