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 the authors´ previous studies to lead to significant improvement in the quality of the reconstructed images. Furthermore, for 3D positron emission tomography, the 3D algebraic reconstruction technique using blobs can reach comparable or even better duality than the 3D filtered backprojection method after only one cycle through the projection data. The only shortcoming of the blob reconstruction is an increased computational demand, because of the overlapping nature of the blobs. These encouraging results mere obtained in the authors´ previous studies for the case when the blobs were placed on the same 3D simple cubic grid used for voxel basis functions. For basis functions which are spherically-symmetric, 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. A good arrangement is the body centered cubic grid. The authors´ studies confirmed that, when using this type of 3D grid, the number of grid points can be effectively reduced, decreasing the computational and memory demands while preserving the quality of the reconstructed images