Cone-beam CT sampling incompleteness: analytical and empirical studies of emerging systems and source-detector orbits

Purpose: Motivated by emerging cone-beam computed tomography (CBCT) systems and scan orbits, we aim to quantitatively assess the completeness of data for 3D image reconstruction-in turn, related to "cone-beam artifacts."Fundamental principles of cone-beam sampling incompleteness are considered with respect to an analytical figure-of-merit [FOM, denoted tanðψminÞ] and related to an empirical FOM (denoted zmod) for measurement of cone-beam artifact magnitude in a test phantom. Approach: A previously proposed analytical FOM [tanðψminÞ, defined as the minimum angle between a point in the 3D image reconstruction and the x-ray source over the scan orbit] was analyzed for a variety of CBCT geometries. A physical test phantom was configured with parallel disk pairs (perpendicular to the z-axis) at various locations throughout the field of view, quantifying cone-beam artifact magnitude in terms of zmod (the relative signal modulation between the disks). Two CBCT systems were considered: an interventional C-arm (Cios Spin 3D; Siemens Healthineers, Forcheim Germany) and a musculoskeletal extremity scanner; Onsight3D, Carestream Health, Rochester, United States)]. Simulations and physical experiments were conducted for various source-detector orbits: (a) a conventional 360 deg circular orbit, (b) tilted and untilted semi-circular (196 deg) orbits, (c) multi-source (three x-ray sources distributed along the z axis) semi-circular orbits, and (d) a non-circular (sine-on-sphere, SoS) orbit. The incompleteness of sampling [tanðψminÞ] and magnitude of cone-beam artifacts (zmod) were evaluated for each system and orbit. Results: The results show visually and quantitatively the effect of system geometry and scan orbit on cone-beam sampling effects, demonstrating the relationship between analytical tanðψminÞ and empirical zmod. Advanced source-detector orbits (e.g., three-source and SoS orbits) exhibited superior sampling completeness as quantified by both the analytical and the empirical FOMs. The test phantom and zmod metric were sensitive to variations in CBCT system geometry and scan orbit and provided a surrogate measure of underlying sampling completeness. Conclusion: For a given system geometry and source-detector orbit, cone-beam sampling completeness can be quantified analytically (in terms arising from Tuy's condition) and/or empirically (using a test phantom for quantification of cone-beam artifacts). Such analysis provides theoretical and practical insight on sampling effects and the completeness of data for emerging CBCT systems and scan trajectories.