Direct filtered-backprojection-type reconstruction from a straight-line trajectory

A computed tomography (CT) imaging configuration with a straight-line trajectory is investigated, and a direct filtered backprojection (FBP) algorithm is presented. This kind of system may be useful for industrial applications and security inspections. Projections from a straight-line trajectory have a special property where data from each detector element correspond to a parallel-beam projection of a certain view angle. However, the sampling steps of parallel beams differ from view to view. Rebinning raw projections into uniformly sampled parallel-beam projections is a common choice for this type of reconstruction problem. However, the rebinning procedure suffers a loss of spatial resolution because of interpolations. Our reconstruction method is first derived from the Fourier slice theorem, where a coordinate transform and geometrical relations in projection and backprojection are used. It is then extended to 3-D scanning geometry. Finally, data-shift preprocessing is proposed to reduce computation and memory requirements by removing useless projections in raw data. In this method, the spatial resolution is better preserved and the reconstruction is less sensitive to data truncation than in the rebinning-to-parallel-beam method. To deal with limited angle problem, an iterative reconstruction reprojection method is introduced to estimate missing data and improve the image quality.