Image representation and tomographic reconstruction using spherically-symmetric volume elements

Spherically symmetric volume elements are alternatives to the more conventional voxels for the construction of volume images in the computer. The use of these volume elements instead of the conventional voxels introduces additional parameters which enable the user to control the smoothness properties of the represented image. The authors have investigated the relationship between the values of these parameters and the properties of the image representation. They also report on their experience with iterative reconstruction algorithms that use these volume elements for the image representation. Experiments with ideal data show that the reconstruction using a blob basis function shows better behavior (mean value, standard deviation, maximum overshoot) in comparison with the classical voxels for objects of dimensions greater than the blob diameter. In the case of X-ray data consistent with the blob model the overshoot is practically eliminated for the blob reconstruction and substantially reduced for the voxel case, and the reconstruction noise is reduced as well