Filtered Backprojection Algorithms Enable Linear Scanning Computed Tomography High-Quality Reconstruction With Large Extended FOVs

For a linear scanning mode - multiple Source Translation Computed Tomography (mSTCT) - when extending a large field-of-view (FOV) with a high geometry magnification, we propose some practical filtered backprojection type reconstruction algorithms. More specially, we formulate a fan-beam Differentiation, Hilbert transform, and Backprojection reconstruction formula for STCT, whose filter is along the detector rather than the source (referred to as D-DHB) to avoid acquiring large amounts of projections, and then generalize it to the cone-beam scene. On the one hand, we apply D-DHB in the full-scan mSTCT (F-mSTCT) mode. On the other hand, we eliminate the unstable position-dependent backprojection weight in the D-DHB formula by introducing an additional weight function. In fact, the backprojection weight of analytical algorithms with filtering along the detector implies the distance between the reconstructed point and the X-ray source focus. Especially where the extended FOV is very close to the source trajectory, removing the position-dependent backprojection weight can avoid some intolerable artifacts around the reconstructed image and improve computation efficiency without losing more accuracy. To meet the requirement of extremely extended FOV imaging, we fully evaluated our two methods from different aspects of the experiments. The results, overall, reveal that our methods are the most practical for mSTCT.