Noise Reduction Using a Theoretically-Exact Algorithm for Helical Cone-Beam Tomography

In this paper we show that the signal-to-noise ratio of helical cone-beam reconstructions based on Katsevish´s formula can be significantly improved for 16- and 32-row scanners, using the observation that Katsevich´s formula heavily relies on the concept of pi-lines. A pi-line is any segment of line that connects two source positions separated by less than one helix turn; pi-lines are such that each point within the helix cylinder belongs to one and only one pi-line. Katsevich´s formula reconstructs the sought density function at a given point using exclusively the data between the two source positions that define the pi-line through this point. We observe that the pi-line through a given point can change significantly when the point is displaced along a direction of the rotation axis of the scanner, and we use this observation to improve image noise as follows: for CT imaging with a prescribed slice thickness Deltaz, we apply Katsevich´s formula to achieve reconstruction on slices separated by a distance Deltaz/M, where M is a positive integer, then obtain any wanted slice as the average of the M closest reconstructed slices. For Katsevich´s formula, proceeding in this way with M large is fundamentally different from reconstructing with M = 1 using pre-smoothing of the data to match the slice thickness target.