Accurate Low-Contrast 3D Cone-Beam Reconstruction With Algebraic Methods

This paper examines the use of the Algebraic Reconstruction Method (ART) and related techniques to reconstruct 3D objects from a relatively sparse set of cone-beam projection data. Although ART has been widely used for cone-beam reconstruction of high-contrast objects, e.g. in computed angiography, we are interested in the more challenging low-con- trast case which represents a little investigated scenario for ART. Preliminary experiments indicate that for cone angles greater than 20˚, traditional ART produces reconstructions with strong aliasing artifacts, obliterating much object detail. By analyzing the reconstruc- tion process using signal processing principles it is revealed that the source of these arti- facts is the non-uniform reconstruction grid sampling of the cone-beam rays. To eliminate these errors, we devise a new way of computing the weights of the reconstruction matrix. This new method is more adequate for cone-beam and replaces the usual constant-size interpolation filter by one whose size is dependent on the source-voxel distance. Doing so enables us to generate alias-free reconstruction at little extra cost. An alternative analysis reveals that Simultaneous ART (SART) has also great potential to produce reconstruction without cone-beam related artifacts, however at greater computational cost. Putting every- thing together, we thoroughly investigate the influence of various ART parameters, such as volume initialization, relaxation coefficient λ, correction scheme, and number of iterations, on reconstruction quality. Using a 3D version of the Shepp-Logan phantom, we find that ART typically requires only three iterations to render a reconstruction result close to the optimum (given proper parameter settings). Thus we conclude that ART is potentially not any costlier than Filtered Backprojection (FBP) techniques, particularly if one considers the fact that ART only requires a fraction of FBP's projection set.