Anti-Aliased 3D Cone-Beam Reconstruction of Low-Contrast Objects with Algebraic Methods

This paper examines the use of the Algebraic Reconstruction Technique (ART) and related techniques to reconstruct 3D objects from a relatively sparse set of cone-beam projections. Although ART has been widely used for cone-beam reconstruction of high-contrast objects, e.g. in computed angiography, the work presented here explores the more challenging low-contrast 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. These artifacts are in addition to the usual off-midplane inaccuracies of cone-beam tomography with planar orbits. We find that the source of these artifacts is the non-uniform reconstruction grid sampling and correction by the conebeam rays during the ART projection/backprojection procedure. A new method to compute the weights of the reconstruction matrix is devised which replaces the usual constant-size interpolation filter by one whose size and amplitude is dependent on the source-voxel distance. This enables the generation of reconstructions free of cone-beam aliasing artifacts at only little extra cost. An alternative analysis reveals that Simultaneous ART (SART) also produces reconstructions without aliasing artifacts, however, at greater computational cost. Finally, we thoroughly investigate the influence of various ART parameters, such as volume initialization, relaxation coefficient λ, correction scheme, number of iterations, and noise in the projection data on reconstruction quality. We find that ART typically requires only three iterations to render satisfactory reconstruction results.