  Recently, an ultra-low-cost linear scan based tomography architecture was
proposed by our team. Similar to linear tomosynthesis, the source and detector
are translated in opposite directions and the data acquisition system targets
on a region-of-interest (ROI) to acquire data for image reconstruction. This
kind of tomography architecture was named parallel translational computed
tomography (PTCT). In our previous studies, filtered backprojection (FBP)-type
algorithms were developed to reconstruct images from PTCT. However, the
reconstructed ROI images from truncated projections have severe truncation
artifacts. In this paper, we propose two backprojection filtering (BPF)-type
algorithms named MP-BPF and MZ-BPF to reconstruct ROI images from truncated
PTCT data. A weight function is constructed to deal with data redundancy for
multi-linear translations modes. Extensive numerical simulations are performed
to evaluate the proposed MP-BPF and MZ-BPF algorithms for PTCT in fan-beam
geometry. Qualitative and quantitative results demonstrate that the proposed
BPF-type algorithms can not only accurately reconstruct ROI images from
truncated projections but also provide high-quality images for the entire image
support in some circumstances.
