Alternatives to voxels for image representation in iterative reconstruction algorithms.

Spherically symmetric volume elements are alternatives to the more conventional voxels for the construction of volume images in the computer. The image representation, and the calculation of projections of it, are essential components of iterative algorithms for image reconstruction from projection data. A two-parameter family of spherical volume elements is described that allows control of the smoothness properties of the represented image, whereas conventional voxels are discontinuous. The rotational symmetry of the spherical elements leads to efficient calculation of projections of the represented image, as required in iterative reconstruction algorithms. For volume elements whose shape is ellipsoidal (rather than spherical) it is shown that efficient calculation of the projections is also possible by means of an image space transformation.