Regions of Backprojection and Comet Tail Artifacts for π-Line Reconstruction Formulas in Tomography

We explore two characteristic features of x-ray computed tomography inversion formulas in two and three dimensions that are dependent on pi-lines. In such formulas the data from a given source position contribute only to the reconstruction of f(x) for x in a certain region, called the region of backprojection. The second characteristic is a certain small artifact in the reconstruction called a comet tail artifact. We propose that the comet tail artifact is closely related to the boundary of the region of backprojection and make this relationship precise, developing a general theory of the region of backprojection, its boundary, and the location of the artifact in helical and fan-beam tomography. This theory is applied to a number of specific examples and confirmed by numerical experiments. Furthermore it is demonstrated that a strong comet tail artifact appears in numerical reconstructions from misaligned fan-beam data. A numerical method for using the artifact to find the correct alignment is suggested.